Analytic Number Theory, Modular Forms and q-Hypergeometric Series

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.

Auteur
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.

Contenu
Manjul Bhargava, Princeton University Squarefree values of polynomial discriminants Ron Graham, University of California San Diego Monochromatic solutions to linear equations Aleksandar Ivic, Serbian Academy of Sciences Hardy's function Z(t) - results and problems Roger Baker, Brigham Young University Limit points and long gaps between primes 1 Dan Goldston, San Jose State University Sums and Differences of Pairs of Primes Helmut Maier, Universit¨at Ulm Recent Results on Gaps between Primes (joint with Michael Th. Rassias) Janos Pintz, MTA R´enyi Institute, Budapest, Hungary On some old conjectures of Paul Erdos on the difference of consecutive primes G´erald Tenenbaum, Universit´e de Lorraine Effective mean-value estimates for complex multiplicative functions Cameron Stewart, University of Waterloo On the abc conjecture Winnie Li, Pennsylvania State University Combinatorial zeta and L-functions James Maynard, University of Oxford Linear equations in primes James Maynard, University of Oxford Talk 2: Prime values of polynomials Wadim Zudilin, University of Newcastle, Australia On certain irrational values of the logarithm: beyond the 1979 limitations Doron Zeilberger, Rutgers University Krishna Alladi's Early Love: Irrationality Measures of Famous Constants Kevin Ford, University of Illinois Large gaps between primes and related problems Kathrin Bringman, University of Cologne Ramanujan and meromorphic modular forms Ken Ono, Emory Unversity Riemann Hypothesis for Period Polynomials of Modular FormsMourad Ismail, University of Central Florida Identities related to the Rogers-Ramanujan identitiesJim Lepowsky, Rutgers University Motivated proofs of generalized Rogers-Ramanujan identities as stimuli for new ideas in vertex operator algebra theory Christian Krattenthaler, University of Vienna Discrete analogues of Macdonald-Mehta integrals