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-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Spis treści
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/π.- 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 New Witness 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.
O autorze
Frank Garvan is a professor of Mathematics at the University of Florida. His research interests are in Number Theory, Basic Hypergeometric Series and Symbolic Computation.
George Andrews is the Evan Pugh University Professor in Mathematics at Penn State University. His research interests are Number Theory and Partitions.
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