Analytic Number Theory, Modular Forms and q-Hypergeometric Series / Andrews, George E. ; Garvan, Frank  

Público ISBD Ningún comentario para este registro. Título : Analytic Number Theory, Modular Forms and q-Hypergeometric Series : In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, March 2016 Tipo de documento: documento electrónico Autores: Andrews, George E., ; Garvan, Frank, Mención de edición: 1 ed. Editorial: [s.l.] : Springer Fecha de publicación: 2017 Número de páginas: L, 736 p. 67 ilustraciones, 11 ilustraciones en color. ISBN/ISSN/DL: 978-3-319-68376-8 Nota general: Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: Teoría de los números Clasificación: 512.7 Resumen: Recopiladas de la Conferencia de Teoría de Números de Gainesville de 2016 en honor a Krishna Alladi en su 60 cumpleaños, estas actas presentan investigaciones recientes en teoría de números. Extenso y detallado, este volumen presenta 40 artículos de destacados investigadores sobre temas de teoría analítica de números, teoría probabilística de números, irracionalidad y trascendencia, análisis diofántico, particiones, series hipergeométricas básicas y formas modulares. Los lectores también encontrarán discusiones detalladas sobre varios aspectos del trabajo innovador de Srinivasa Ramanujan y su influencia en la investigación actual. Muchos de los artículos fueron motivados por la propia investigación de Alladi sobre particiones y series q, así como por su trabajo anterior en teoría de números. Alladi es bien conocido por sus contribuciones en teoría de números y matemáticas. Sus intereses de investigación incluyen combinatoria, matemáticas discretas, métodos de tamiz, teoría analítica y probabilística de números, aproximaciones diofánticas, particiones e identidades de series q. Los estudiantes de posgrado e investigadores encontrarán en este volumen un recurso valioso sobre nuevos desarrollos en diversos aspectos de la teoría de números. Nota de contenido: Preface -- List of Participants -- Plus-Minus Weighted Zero-Sum Constants: A Survey.- Vector-valued Modular Forms and the Seventh Order Mock Theta Functions.- The Alladi-Schur Polynomials and Their Factorization.- New Representations for s(q) via Reciprocity Theorems.- Mean Values of the Functional Equation Factors at the Zeros of Derivatives of the Riemann Zeta Function and Dirichlet L-Functions.- New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions.- The Appearance of H. F. Baker and E. W. Hobson in "The Man Who Knew Infinity".- A Bibasic Heine Transformation Formula and Ramanujan's 2f1 Transformations.- Adventures with the OEIS.- Three-Colored Partitions and Dilated Companions of Capparelli's Identities.- Nearly Equal Distributions of the Rank and the Crank of Partitions.- Holonomic Alchemy and Series for 1/Ï€ -- Integral Points on a Very Flat Convex Curve -- Unification, Refinements and Companions of Generalisations of Schur's Theorem -- Integrals Involving Rudin-Shapiro Polynomials and Sketch of a Proof of Saffari's Conjecture -- From Ramanujan to Groups of Rationals: A personal history of abstract multiplicative functions.- On an Additive Prime Divisor Function of Alladi and Erdos.- Ramanujan's Tau Function.- Construction of Cusp Forms Using Rankin-Cohen Brackets.- An Open Problem of Corteel, Lovejoy, and Mallet.- On the Asymptotics of Partial Theta Functions.- Overpartitions and Truncated Partition Identities -- Congruences Modulo Powers of 2 for the Number of Unique Path Partitions.- Complex Form of Classical and Quantum Electrodynamics -- On a System of q-Partial Differential Equations with Applications to q-Series.- Asymmetric Generalizations of Schur's theorem -- Local Behavior of the Composition of the Aliquot and Co-Totient Functions.- On the Universal Mock Theta Function g2 and Zwegers' μ-function -- Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series.- Littlewood Polynomials -- Trapezoidal Numbers, Divisor Functions, and a Partition Theorem of Sylvester -- Estimates of li(q(x))−p(x) and the Riemann Hypothesis.- Partition-Theoretic Formulas for Arithmetic Densities.- A NewWitness Identity for 11 / p(11n+6) -- On the Representations of a Positive Integer by Certain Classes of Quadratic Forms in Eight Variables.- A Note on Thue Inequalities with Few Coefficients.- Basic Hypergeometric Summations from Rook Theory.- Overpartitions and Singular Overpartitions -- A Classical q-Hypergeometric Approach to the A (2) 2 Standard Modules -- Generalized Mertens Sums. . Tipo de medio : Computadora Summary : Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory.  Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-seriesidentities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...] Analytic Number Theory, Modular Forms and q-Hypergeometric Series : In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, March 2016 [documento electrónico] / Andrews, George E., ; Garvan, Frank,  . -  1 ed.  . - [s.l.] : Springer, 2017 . - L, 736 p. 67 ilustraciones, 11 ilustraciones en color. ISBN : 978-3-319-68376-8 Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: Teoría de los números Clasificación: 512.7 Resumen: Recopiladas de la Conferencia de Teoría de Números de Gainesville de 2016 en honor a Krishna Alladi en su 60 cumpleaños, estas actas presentan investigaciones recientes en teoría de números. Extenso y detallado, este volumen presenta 40 artículos de destacados investigadores sobre temas de teoría analítica de números, teoría probabilística de números, irracionalidad y trascendencia, análisis diofántico, particiones, series hipergeométricas básicas y formas modulares. Los lectores también encontrarán discusiones detalladas sobre varios aspectos del trabajo innovador de Srinivasa Ramanujan y su influencia en la investigación actual. Muchos de los artículos fueron motivados por la propia investigación de Alladi sobre particiones y series q, así como por su trabajo anterior en teoría de números. Alladi es bien conocido por sus contribuciones en teoría de números y matemáticas. Sus intereses de investigación incluyen combinatoria, matemáticas discretas, métodos de tamiz, teoría analítica y probabilística de números, aproximaciones diofánticas, particiones e identidades de series q. Los estudiantes de posgrado e investigadores encontrarán en este volumen un recurso valioso sobre nuevos desarrollos en diversos aspectos de la teoría de números. Nota de contenido: Preface -- List of Participants -- Plus-Minus Weighted Zero-Sum Constants: A Survey.- Vector-valued Modular Forms and the Seventh Order Mock Theta Functions.- The Alladi-Schur Polynomials and Their Factorization.- New Representations for s(q) via Reciprocity Theorems.- Mean Values of the Functional Equation Factors at the Zeros of Derivatives of the Riemann Zeta Function and Dirichlet L-Functions.- New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions.- The Appearance of H. F. Baker and E. W. Hobson in "The Man Who Knew Infinity".- A Bibasic Heine Transformation Formula and Ramanujan's 2f1 Transformations.- Adventures with the OEIS.- Three-Colored Partitions and Dilated Companions of Capparelli's Identities.- Nearly Equal Distributions of the Rank and the Crank of Partitions.- Holonomic Alchemy and Series for 1/Ï€ -- Integral Points on a Very Flat Convex Curve -- Unification, Refinements and Companions of Generalisations of Schur's Theorem -- Integrals Involving Rudin-Shapiro Polynomials and Sketch of a Proof of Saffari's Conjecture -- From Ramanujan to Groups of Rationals: A personal history of abstract multiplicative functions.- On an Additive Prime Divisor Function of Alladi and Erdos.- Ramanujan's Tau Function.- Construction of Cusp Forms Using Rankin-Cohen Brackets.- An Open Problem of Corteel, Lovejoy, and Mallet.- On the Asymptotics of Partial Theta Functions.- Overpartitions and Truncated Partition Identities -- Congruences Modulo Powers of 2 for the Number of Unique Path Partitions.- Complex Form of Classical and Quantum Electrodynamics -- On a System of q-Partial Differential Equations with Applications to q-Series.- Asymmetric Generalizations of Schur's theorem -- Local Behavior of the Composition of the Aliquot and Co-Totient Functions.- On the Universal Mock Theta Function g2 and Zwegers' μ-function -- Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series.- Littlewood Polynomials -- Trapezoidal Numbers, Divisor Functions, and a Partition Theorem of Sylvester -- Estimates of li(q(x))−p(x) and the Riemann Hypothesis.- Partition-Theoretic Formulas for Arithmetic Densities.- A NewWitness Identity for 11 / p(11n+6) -- On the Representations of a Positive Integer by Certain Classes of Quadratic Forms in Eight Variables.- A Note on Thue Inequalities with Few Coefficients.- Basic Hypergeometric Summations from Rook Theory.- Overpartitions and Singular Overpartitions -- A Classical q-Hypergeometric Approach to the A (2) 2 Standard Modules -- Generalized Mertens Sums. . Tipo de medio : Computadora Summary : Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory.  Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-seriesidentities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...]

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