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Analytic Number Theory, Modular Forms and q-Hypergeometric Series

In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, March 2016

  • Conference proceedings
  • © 2017

Overview

Editors:
  1. George E. Andrews

    1. Department of Mathematics, Pennsylvania State University, State College, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Frank Garvan

    1. Department of Mathematics, University of Florida, Gainesville, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Offers numerous and diverse articles on the latest research in number theory
  • Expands on Krishna Alladi's recent contributions on partitions and q-series

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 221)

Included in the following conference series:

Conference proceedings info: ALLADI60 2016.

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Table of contents (40 papers)

  1. Front Matter

    Pages i-l
    Download chapter PDF

  2. Plus-Minus Weighted Zero-Sum Constants: A Survey

    • Sukumar Das Adhikari
    Pages 1-9

  3. Vector-valued Modular Forms and the Seventh Order Mock Theta Functions

    • Nickolas Andersen
    Pages 11-23

  4. The Alladi–Schur Polynomials and Their Factorization

    • George E. Andrews
    Pages 25-38

  5. New Representations for \(\sigma (q)\) via Reciprocity Theorems

    • Koustav Banerjee, Atul Dixit
    Pages 39-57

  6. Mean Values of the Functional Equation Factors at the Zeros of Derivatives of the Riemann Zeta Function and Dirichlet L-Functions

    • Kübra Benli, Ertan Elma, Cem Yalçın Yıldırım
    Pages 59-67

  7. New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions

    • Alexander Berkovich, Ali Kemal Uncu
    Pages 69-94

  8. The Appearance of H.F. Baker and E.W. Hobson in “The Man Who Knew Infinity”

    • Bruce C. Berndt
    Pages 95-97

  9. A Bibasic Heine Transformation Formula and Ramanujan’s \(_2\phi _1\) Transformations

    • Gaurav Bhatnagar
    Pages 99-122

  10. Adventures with the OEIS

    • Jonathan M. Borwein
    Pages 123-138

  11. Three-Colored Partitions and Dilated Companions of Capparelli’s Identities

    • Kathrin Bringmann, Karl Mahlburg
    Pages 139-156

  12. Nearly Equal Distributions of the Rank and the Crank of Partitions

    • William Y. C. Chen, Kathy Q. Ji, Wenston J. T. Zang
    Pages 157-177

  13. Holonomic Alchemy and Series for \(1/\pi \)

    • Shaun Cooper, James G. Wan, Wadim Zudilin
    Pages 179-205

  14. Integral Points on a Very Flat Convex Curve

    • Jean-Marc Deshouillers, Georges Grekos
    Pages 207-212

  15. Unification, Refinements and Companions of Generalisations of Schur’s Theorem

    • Jehanne Dousse
    Pages 213-251

  16. Integrals Involving Rudin–Shapiro Polynomials and Sketch of a Proof of Saffari’s Conjecture

    • Shalosh B. Ekhad, Doron Zeilberger
    Pages 253-265

  17. From Ramanujan to Groups of Rationals: A Personal History of Abstract Multiplicative Functions

    • P. D. T. A. Elliott
    Pages 267-295

  18. On an Additive Prime Divisor Function of Alladi and Erdős

    • Dorian Goldfeld
    Pages 297-309

  19. Ramanujan’s Tau Function

    • Michael D. Hirschhorn
    Pages 311-328

  20. Construction of Cusp Forms Using Rankin–Cohen Brackets

    • Abhash Kumar Jha, Arvind Kumar
    Pages 329-341
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  1. Analytic Number Theory, Modular Forms and q-Hypergeometric Series

Keywords

About this book

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.


Editors and Affiliations

  • Department of Mathematics, Pennsylvania State University, State College, USA

    George E. Andrews

  • Department of Mathematics, University of Florida, Gainesville, USA

    Frank Garvan

About the editors

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.

Bibliographic Information

  • Book Title: Analytic Number Theory, Modular Forms and q-Hypergeometric Series

  • Book Subtitle: In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, March 2016

  • Editors: George E. Andrews, Frank Garvan

  • Series Title: Springer Proceedings in Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-3-319-68376-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-68375-1Published: 04 February 2018

  • Softcover ISBN: 978-3-319-88592-6Published: 06 June 2019

  • eBook ISBN: 978-3-319-68376-8Published: 01 February 2018

  • Series ISSN: 2194-1009

  • Series E-ISSN: 2194-1017

  • Edition Number: 1

  • Number of Pages: L, 736

  • Number of Illustrations: 56 b/w illustrations, 11 illustrations in colour

  • Topics: Number Theory

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