Dewey Class 
512.7 
Title 
Analytic Number Theory, Modular Forms and qHypergeometric Series ([EBook]) : In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, March 2016 / / edited by George E. Andrews, Frank Garvan. 
Added Personal Name 
Andrews, George E. editor. 
Garvan, Frank editor. 
Other name(s) 
SpringerLink (Online service) 
Publication 
Cham : : Springer International Publishing : : Imprint: Springer, , 2017. 
Physical Details 
L, 736 p. 67 illus., 11 illus. in color. : online resource. 
Series 
Springer Proceedings in Mathematics & Statistics 21941009 ; ; 221 
ISBN 
9783319683768 
Summary Note 
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 pathbreaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and qseries 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 qseries identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.: 
Contents note 
Preface  List of Participants  PlusMinus Weighted ZeroSum Constants: A Survey. Vectorvalued Modular Forms and the Seventh Order Mock Theta Functions. The AlladiSchur 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 LFunctions. 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. ThreeColored 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/π  Integral Points on a Very Flat Convex Curve  Unification, Refinements and Companions of Generalisations of Schur’s Theorem  Integrals Involving RudinShapiro 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 RankinCohen 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 qPartial Differential Equations with Applications to qSeries. Asymmetric Generalizations of Schur’s theorem  Local Behavior of the Composition of the Aliquot and CoTotient Functions. On the Universal Mock Theta Function g2 and Zwegers’ μfunction  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. PartitionTheoretic 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 qHypergeometric Approach to the A (2) 2 Standard Modules  Generalized Mertens Sums. . 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9783319683768 
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