Analytic Number Theory, Modular Forms and Q-Hypergeometric Series: In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, Mar

ISBN-13: 9783319683751 / Angielski / Twarda / 2018 / 736 str.

Frank Garvan; George Andrews

Opis

Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory.

Spis treści

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 Erd˝os 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 c

onjecture 

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 Forms

Mourad Ismail, University of Central Florida Identities related to the Rogers-Ramanujan identities

Jim Lepowsky, Rutgers University “Motivated proofs” of generalized Rogers-Ramanujan identities as stimuli for new ideas in vertex ope

rator algebra theory  Christian Krattenthaler, University of Vienna Discrete analogues of Macdonald-Mehta integrals

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.

Blurb

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.