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Título : Number Theory and Related Fields : In Memory of Alf van der Poorten Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Jonathan M. Borwein ; Shparlinski, Igor ; Zudilin, Wadim Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009 num. 43 Número de páginas: X, 395 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-6642-0 Idioma : Inglés (eng) Palabras clave: Mathematics Number theory Theory Clasificación: 51 Matemáticas Resumen: Number Theory and Related Fields collects contributions based on the proceedings of the “International Number Theory Conference in Memory of Alf van der Poorten,” hosted by CARMA and held March 12–16, 2012, at the University of Newcastle, Australia. The purpose of the conference was to commemorate the research and influence of Alf van der Poorten in number theory and in general mathematics and presented an exciting venue for promoting number-theoretic research and graduate study in Australia. Comprehensive accounts of recent achievements in theoretical and computational number theory and its applications to cryptography and theoretical computer science were also paramount to the conference. The volume begins with a detailed academic appreciation of van der Poorten’s life and work, and includes research articles written by some of the most distinguished mathematicians in the field of number theory. Contributions also include related topics that focus on the various research interests of van der Poorten, such as continued fractions and elliptic curves. Researchers in number theory and its applications will find this Proceedings of great interest Nota de contenido: Preface -- Life and Mathematics of Alfred Jacobus van der Poorten (D. Hunt) -- Ramanujan-Sato-Like Series (G. Almkvist, J. Guillera) -- On the Sign of the Real Part of the Riemann Zeta Function (J. Arias de Reyna, R.P. Brent, J. van de Lune) -- Additive Combinatorics with a View Toward Computer Science and Cryptography (K. Bibak) -- Transcendence of Stammering Continued Fractions (Y. Bugeaud) -- Algebraic Independence of Infinite Products and Their Derivatives (P. Bundschuh) -- Small Representations by Indefinite Ternary Quadratic Forms (J.B. Friedlander, H. Iwaniec) -- Congruences for Andrews' SPT-Function Modulo 32760 and Extension of Atkin's Hecke-Type Partition Congruences (F.G. Garvan) -- Continued Fractions and Dedekind Sums for Function Fields (Y. Hamahata) -- Burgess's Bounds for Character Sums (D.R. Heath-Brown).-Structured Hadamard Conjecture (I.S. Kotsireas) -- Families of Cubic Thue Equations with Effective Bounds for the Solutions (C. Levesque, M. Waldschmidt) -- Consequences of a Factorization Theorem for Generalized Exponential Polynomials with Infinitely Many Integer Zeros (V. Laohakosol, O. Phuksuwan) -- On Balanced Subgroups of the Multiplicative Group (C. Pomerance, D. Ulmer) -- Some Extensions of the Lucas Functions (E.L. Roettger, H.C. Williams, R.K. Guy) -- The Impact of Number Theory and Computer-Aided Mathematics on Solving the Hadamard Matrix Conjecture (J. Seberry) -- Description of Generalized Continued Fractions by Finite Automata (J. Shallit) -- Some Notes on Weighted Sum Formulae for Double Zeta Values (J. Wan) -- Period(d)ness of L-Values (W. Zudilin) En línea: http://dx.doi.org/10.1007/978-1-4614-6642-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32312 Number Theory and Related Fields : In Memory of Alf van der Poorten [documento electrónico] / SpringerLink (Online service) ; Jonathan M. Borwein ; Shparlinski, Igor ; Zudilin, Wadim . - New York, NY : Springer New York : Imprint: Springer, 2013 . - X, 395 p : online resource. - (Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009; 43) .
ISBN : 978-1-4614-6642-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Number theory Theory Clasificación: 51 Matemáticas Resumen: Number Theory and Related Fields collects contributions based on the proceedings of the “International Number Theory Conference in Memory of Alf van der Poorten,” hosted by CARMA and held March 12–16, 2012, at the University of Newcastle, Australia. The purpose of the conference was to commemorate the research and influence of Alf van der Poorten in number theory and in general mathematics and presented an exciting venue for promoting number-theoretic research and graduate study in Australia. Comprehensive accounts of recent achievements in theoretical and computational number theory and its applications to cryptography and theoretical computer science were also paramount to the conference. The volume begins with a detailed academic appreciation of van der Poorten’s life and work, and includes research articles written by some of the most distinguished mathematicians in the field of number theory. Contributions also include related topics that focus on the various research interests of van der Poorten, such as continued fractions and elliptic curves. Researchers in number theory and its applications will find this Proceedings of great interest Nota de contenido: Preface -- Life and Mathematics of Alfred Jacobus van der Poorten (D. Hunt) -- Ramanujan-Sato-Like Series (G. Almkvist, J. Guillera) -- On the Sign of the Real Part of the Riemann Zeta Function (J. Arias de Reyna, R.P. Brent, J. van de Lune) -- Additive Combinatorics with a View Toward Computer Science and Cryptography (K. Bibak) -- Transcendence of Stammering Continued Fractions (Y. Bugeaud) -- Algebraic Independence of Infinite Products and Their Derivatives (P. Bundschuh) -- Small Representations by Indefinite Ternary Quadratic Forms (J.B. Friedlander, H. Iwaniec) -- Congruences for Andrews' SPT-Function Modulo 32760 and Extension of Atkin's Hecke-Type Partition Congruences (F.G. Garvan) -- Continued Fractions and Dedekind Sums for Function Fields (Y. Hamahata) -- Burgess's Bounds for Character Sums (D.R. Heath-Brown).-Structured Hadamard Conjecture (I.S. Kotsireas) -- Families of Cubic Thue Equations with Effective Bounds for the Solutions (C. Levesque, M. Waldschmidt) -- Consequences of a Factorization Theorem for Generalized Exponential Polynomials with Infinitely Many Integer Zeros (V. Laohakosol, O. Phuksuwan) -- On Balanced Subgroups of the Multiplicative Group (C. Pomerance, D. Ulmer) -- Some Extensions of the Lucas Functions (E.L. Roettger, H.C. Williams, R.K. Guy) -- The Impact of Number Theory and Computer-Aided Mathematics on Solving the Hadamard Matrix Conjecture (J. Seberry) -- Description of Generalized Continued Fractions by Finite Automata (J. Shallit) -- Some Notes on Weighted Sum Formulae for Double Zeta Values (J. Wan) -- Period(d)ness of L-Values (W. Zudilin) En línea: http://dx.doi.org/10.1007/978-1-4614-6642-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32312 Ejemplares
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Título : Number Theory : Structures, Examples, and Problems Tipo de documento: documento electrónico Autores: Dorin Andrica ; SpringerLink (Online service) ; Titu Andreescu Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2009 Número de páginas: XVIII, 384 p. 2 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4645-5 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Number theory Combinatorics Theory Mathematics, general Clasificación: 51 Matemáticas Resumen: Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This lively introductory text focuses on a problem-solving approach to the subject. Key features of Number Theory: Structures, Examples, and Problems: * A rigorous exposition starts with the natural numbers and the basics. * Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties. * Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered. * Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems. * Glossary, bibliography, and comprehensive index round out the text. Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels Nota de contenido: Fundamentals -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous Problems -- Solutions to Additional Problems -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous Problems En línea: http://dx.doi.org/10.1007/b11856 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33936 Number Theory : Structures, Examples, and Problems [documento electrónico] / Dorin Andrica ; SpringerLink (Online service) ; Titu Andreescu . - Boston : Birkhäuser Boston, 2009 . - XVIII, 384 p. 2 illus : online resource.
ISBN : 978-0-8176-4645-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Number theory Combinatorics Theory Mathematics, general Clasificación: 51 Matemáticas Resumen: Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This lively introductory text focuses on a problem-solving approach to the subject. Key features of Number Theory: Structures, Examples, and Problems: * A rigorous exposition starts with the natural numbers and the basics. * Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties. * Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered. * Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems. * Glossary, bibliography, and comprehensive index round out the text. Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels Nota de contenido: Fundamentals -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous Problems -- Solutions to Additional Problems -- Divisibility -- Powers of Integers -- Floor Function and Fractional Part -- Digits of Numbers -- Basic Principles in Number Theory -- Arithmetic Functions -- More on Divisibility -- Diophantine Equations -- Some Special Problems in Number Theory -- Problems Involving Binomial Coefficients -- Miscellaneous Problems En línea: http://dx.doi.org/10.1007/b11856 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33936 Ejemplares
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Título : Number Theory : Tradition and Modernization Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Zhang, Wenpeng ; Tanigawa, Yoshio Editorial: Boston, MA : Springer US Fecha de publicación: 2006 Colección: Developments in Mathematics, ISSN 1389-2177 num. 15 Número de páginas: XXII, 234 p Il.: online resource ISBN/ISSN/DL: 978-0-387-30829-6 Idioma : Inglés (eng) Palabras clave: Mathematics Approximation theory Fourier analysis Special functions Number Theory Functions Approximations and Expansions Analysis Clasificación: 51 Matemáticas Resumen: Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples. The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects. Audience This book is intended for researchers and graduate students in analytic number theory Nota de contenido: Positive Finiteness of Number Systems -- On a Distribution Property of the Residual Order of a (mod p)— IV -- Diagonalizing “Bad” Hecke Operators on Spaces of Cusp Forms -- On the Hilbert-Kamke and the Vinogradov Problems in Additive Number Theory -- The Goldbach-Vinogradov Theorem in Arithmetic Progressions -- Densities of Sets of Primes Related to Decimal Expansion of Rational Numbers -- Spherical Functions on p-Adic Homogeneous Spaces -- On Modular forms of Weight (6n + 1)/5 Satisfying a Certain Differential Equation -- Some Aspects of the Modular Relation -- Zeros of Automorphic L-Functions and Noncyclic Base Change -- Analytic Properties of Multiple Zeta-Functions in Several Variables -- Cubic Fields and Mordell Curves -- Towards the Reciprocity of Quartic Theta-Weyl Sums, and Beyond -- Explicit Congruences for Euler Polynomials -- Square-Free Integers as Sums of Two Squares -- Some Applications of L-Functions to the Mean Value of the Dedekind Sums and Cochrane Sums En línea: http://dx.doi.org/10.1007/0-387-30829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34775 Number Theory : Tradition and Modernization [documento electrónico] / SpringerLink (Online service) ; Zhang, Wenpeng ; Tanigawa, Yoshio . - Boston, MA : Springer US, 2006 . - XXII, 234 p : online resource. - (Developments in Mathematics, ISSN 1389-2177; 15) .
ISBN : 978-0-387-30829-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Approximation theory Fourier analysis Special functions Number Theory Functions Approximations and Expansions Analysis Clasificación: 51 Matemáticas Resumen: Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples. The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects. Audience This book is intended for researchers and graduate students in analytic number theory Nota de contenido: Positive Finiteness of Number Systems -- On a Distribution Property of the Residual Order of a (mod p)— IV -- Diagonalizing “Bad” Hecke Operators on Spaces of Cusp Forms -- On the Hilbert-Kamke and the Vinogradov Problems in Additive Number Theory -- The Goldbach-Vinogradov Theorem in Arithmetic Progressions -- Densities of Sets of Primes Related to Decimal Expansion of Rational Numbers -- Spherical Functions on p-Adic Homogeneous Spaces -- On Modular forms of Weight (6n + 1)/5 Satisfying a Certain Differential Equation -- Some Aspects of the Modular Relation -- Zeros of Automorphic L-Functions and Noncyclic Base Change -- Analytic Properties of Multiple Zeta-Functions in Several Variables -- Cubic Fields and Mordell Curves -- Towards the Reciprocity of Quartic Theta-Weyl Sums, and Beyond -- Explicit Congruences for Euler Polynomials -- Square-Free Integers as Sums of Two Squares -- Some Applications of L-Functions to the Mean Value of the Dedekind Sums and Cochrane Sums En línea: http://dx.doi.org/10.1007/0-387-30829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34775 Ejemplares
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Título : Number Fields and Function Fields—Two Parallel Worlds Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Geer, Gerard van der ; Moonen, Ben ; Schoof, René Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Progress in Mathematics num. 239 Número de páginas: XIII, 321 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4447-5 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Number theory Physics Geometry Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights in the more arithmetically-oriented world of number fields, or vice versa. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives. This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections. Contributors: G. Böckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Köhler; U. Kühn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner Nota de contenido: Arithmetic over Function Fields: A Cohomological Approach -- Algebraic Stacks Whose Number of Points over Finite Fields is a Polynomial -- On a Problem of Miyaoka -- Monodromy Groups Associated to Non-Isotrivial Drinfeld Modules in Generic Characteristic -- Irreducible Values of Polynomials: A Non-Analogy -- Schemes over -- Line Bundles and p-Adic Characters -- Arithmetic Eisenstein Classes on the Siegel Space: Some Computations -- Uniformizing the Stacks of Abelian Sheaves -- Faltings’ Delta-Invariant of a Hyperelliptic Riemann Surface -- A Hirzebruch Proportionality Principle in Arakelov Geometry -- On the Height Conjecture for Algebraic Points on Curves Defined over Number Fields -- A Note on Absolute Derivations and Zeta Functions -- On the Order of Certain Characteristic Classes of the Hodge Bundle of Semi-Abelian Schemes -- A Note on the Manin-Mumford Conjecture En línea: http://dx.doi.org/10.1007/0-8176-4447-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35194 Number Fields and Function Fields—Two Parallel Worlds [documento electrónico] / SpringerLink (Online service) ; Geer, Gerard van der ; Moonen, Ben ; Schoof, René . - Boston, MA : Birkhäuser Boston, 2005 . - XIII, 321 p : online resource. - (Progress in Mathematics; 239) .
ISBN : 978-0-8176-4447-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Number theory Physics Geometry Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights in the more arithmetically-oriented world of number fields, or vice versa. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives. This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections. Contributors: G. Böckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Köhler; U. Kühn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner Nota de contenido: Arithmetic over Function Fields: A Cohomological Approach -- Algebraic Stacks Whose Number of Points over Finite Fields is a Polynomial -- On a Problem of Miyaoka -- Monodromy Groups Associated to Non-Isotrivial Drinfeld Modules in Generic Characteristic -- Irreducible Values of Polynomials: A Non-Analogy -- Schemes over -- Line Bundles and p-Adic Characters -- Arithmetic Eisenstein Classes on the Siegel Space: Some Computations -- Uniformizing the Stacks of Abelian Sheaves -- Faltings’ Delta-Invariant of a Hyperelliptic Riemann Surface -- A Hirzebruch Proportionality Principle in Arakelov Geometry -- On the Height Conjecture for Algebraic Points on Curves Defined over Number Fields -- A Note on Absolute Derivations and Zeta Functions -- On the Order of Certain Characteristic Classes of the Hodge Bundle of Semi-Abelian Schemes -- A Note on the Manin-Mumford Conjecture En línea: http://dx.doi.org/10.1007/0-8176-4447-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35194 Ejemplares
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Título : Number Theory : An Introduction to Mathematics Tipo de documento: documento electrónico Autores: William A. Coppel ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: Universitext, ISSN 0172-5939 Número de páginas: XIV, 610 p. 17 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-89486-7 Idioma : Inglés (eng) Palabras clave: Mathematics Number theory Theory Mathematics, general Clasificación: 51 Matemáticas Resumen: "Number Theory" is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse–Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study. From the reviews: "This is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics." —Canadian Mathematical Society "As a source for information on the 'reach' of number theory into other areas of mathematics, it is an excellent work." —Mathematical Association of America Nota de contenido: The Expanding Universe of Numbers -- Divisibility -- More on Divisibility -- Continued Fractions and Their Uses -- Hadamard#x2019;s Determinant Problem -- Hensel#x2019;s -adic Numbers -- The Arithmetic of Quadratic Forms -- The Geometry of Numbers -- The Number of Prime Numbers -- A Character Study -- Uniform Distribution and Ergodic Theory -- Elliptic Functions -- Connections with Number Theory En línea: http://dx.doi.org/10.1007/978-0-387-89486-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33916 Number Theory : An Introduction to Mathematics [documento electrónico] / William A. Coppel ; SpringerLink (Online service) . - New York, NY : Springer New York, 2009 . - XIV, 610 p. 17 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-0-387-89486-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Number theory Theory Mathematics, general Clasificación: 51 Matemáticas Resumen: "Number Theory" is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse–Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study. From the reviews: "This is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics." —Canadian Mathematical Society "As a source for information on the 'reach' of number theory into other areas of mathematics, it is an excellent work." —Mathematical Association of America Nota de contenido: The Expanding Universe of Numbers -- Divisibility -- More on Divisibility -- Continued Fractions and Their Uses -- Hadamard#x2019;s Determinant Problem -- Hensel#x2019;s -adic Numbers -- The Arithmetic of Quadratic Forms -- The Geometry of Numbers -- The Number of Prime Numbers -- A Character Study -- Uniform Distribution and Ergodic Theory -- Elliptic Functions -- Connections with Number Theory En línea: http://dx.doi.org/10.1007/978-0-387-89486-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33916 Ejemplares
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