Andrews, George E.

Analytic Number Theory, Modular Forms and q-Hypergeometric Series

Andrews, George E. - Analytic Number Theory, Modular Forms and q-Hypergeometric Series, ebook


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Table of contents

1. Plus-Minus Weighted Zero-Sum Constants: A Survey
Sukumar Das Adhikari

2. Vector-valued Modular Forms and the Seventh Order Mock Theta Functions
Nickolas Andersen

3. The Alladi–Schur Polynomials and Their Factorization
George E. Andrews

4. New Representations for

Koustav Banerjee, Atul Dixit

5. 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

6. New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions
Alexander Berkovich, Ali Kemal Uncu

7. The Appearance of H.F. Baker and E.W. Hobson in “The Man Who Knew Infinity”
Bruce C. Berndt

8. A Bibasic Heine Transformation Formula and Ramanujan’s

Gaurav Bhatnagar

9. Adventures with the OEIS
Jonathan M. Borwein

10. Three-Colored Partitions and Dilated Companions of Capparelli’s Identities
Kathrin Bringmann, Karl Mahlburg

11. Nearly Equal Distributions of the Rank and the Crank of Partitions
William Y. C. Chen, Kathy Q. Ji, Wenston J. T. Zang

12. Holonomic Alchemy and Series for

Shaun Cooper, James G. Wan, Wadim Zudilin

13. Integral Points on a Very Flat Convex Curve
Jean-Marc Deshouillers, Georges Grekos

14. Unification, Refinements and Companions of Generalisations of Schur’s Theorem
Jehanne Dousse

15. Integrals Involving Rudin–Shapiro Polynomials and Sketch of a Proof of Saffari’s Conjecture
Shalosh B. Ekhad, Doron Zeilberger

16. From Ramanujan to Groups of Rationals: A Personal History of Abstract Multiplicative Functions
P. D. T. A. Elliott

17. On an Additive Prime Divisor Function of Alladi and Erdős
Dorian Goldfeld

18. Ramanujan’s Tau Function
Michael D. Hirschhorn

19. Construction of Cusp Forms Using Rankin–Cohen Brackets
Abhash Kumar Jha, Arvind Kumar

20. An Open Problem of Corteel, Lovejoy, and Mallet
Shashank Kanade, Kağan Kurşungöz, Matthew Russell

21. On the Asymptotics of Partial Theta Functions
Susie Kimport

22. Overpartitions and Truncated Partition Identities
Louis W. Kolitsch

23. Congruences Modulo Powers of 2 for the Number of Unique Path Partitions
C. Krattenthaler

24. Complex Form of Classical and Quantum Electrodynamics
Sergey I. Kryuchkov, Nathan A. Lanfear, Sergei K. Suslov

25. On a System of q-Partial Differential Equations with Applications to q-Series
Zhi-Guo Liu

26. Asymmetric Generalizations of Schur’s Theorem
Jeremy Lovejoy

27. Local Behavior of the Composition of the Aliquot and Co-Totient Functions
Florian Luca, Carl Pomerance

28. On the Universal Mock Theta Function

Richard J. McIntosh

29. Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series
James Mc Laughlin

30. Littlewood Polynomials
Hugh L. Montgomery

31. Trapezoidal Numbers, Divisor Functions, and a Partition Theorem of Sylvester
Melvyn B. Nathanson

32. Estimates of

Jean-Louis Nicolas

33. Partition-Theoretic Formulas for Arithmetic Densities
Ken Ono, Robert Schneider, Ian Wagner

34. A New Witness Identity for

Peter Paule, Cristian-Silviu Radu

35. On the Representations of a Positive Integer by Certain Classes of Quadratic Forms in Eight Variables
B. Ramakrishnan, Brundaban Sahu, Anup Kumar Singh

36. A Note on Thue Inequalities with Few Coefficients
N. Saradha, Divyum Sharma

37. Basic Hypergeometric Summations from Rook Theory
Michael J. Schlosser, Meesue Yoo

38. Overpartitions and Singular Overpartitions
Seunghyun Seo, Ae Ja Yee

39. A Classical q-Hypergeometric Approach to the

Andrew V. Sills

40. Generalized Mertens Sums
Gérald Tenenbaum

Keywords: Mathematics, Number Theory

Publication year
Springer Proceedings in Mathematics & Statistics
Page amount
50 pages
Natural Sciences
Printed ISBN

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