**Contemporary Mathematics**

Volume: 627;
2014;
174 pp;
Softcover

MSC: Primary 05; 11; 14; 17; 30; 33;

Print ISBN: 978-1-4704-1078-0

Product Code: CONM/627

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

**Electronic ISBN: 978-1-4704-2039-0
Product Code: CONM/627.E**

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

# Ramanujan 125

Share this page *Edited by *
*Krishnaswami Alladi; Frank Garvan; Ae Ja Yee*

This volume contains the proceedings of an international conference to
commemorate the 125th anniversary of Ramanujan's birth, held from
November 5–7, 2012, at the University of Florida, Gainesville,
Florida.

Srinivasa Ramanujan was India's most famous mathematician. This
volume contains research and survey papers describing recent and
current developments in the areas of mathematics influenced by
Ramanujan. The topics covered include modular forms, mock theta
functions and harmonic Maass forms, continued fractions, partition
inequalities, \(q\)-series, representations of affine Lie algebras and
partition identities, highly composite numbers, analytic number theory
and quadratic forms.

#### Readership

Graduate students and research mathematicians interested in number theory.

# Table of Contents

## Ramanujan 125

- Cover Cover11 free
- Title page iii4 free
- Preface vii8 free
- Hecke grids and congruences for weakly holomorphic modular forms 112 free
- Knots and 𝑞-series 1728
- A partition inequality involving products of two 𝑞-Pochhammer symbols 2536
- Analogues of Koshliakov’s formula 4152
- How to prove Ramanujan’s 𝑞-continued fractions 4960
- 1. Introduction 4960
- 2. Euler’s approach 5061
- 3. The Rogers-Ramanujan Continued Fraction 5061
- 4. Convergence matters 5364
- 5. More continued fractions by Euler’s approach 5768
- 6. The role of transformation formulas 6071
- 7. A dose of insight into algebraical formulae 6374
- 8. Infinite products as continued fractions 6576
- 9. Conclusion 6778
- References 6778

- A nonsingular 𝑍₃ curve of genus 4 6980
- Ramanujan’s radial limits 91102
- An identity that may have changed the course of history 103114
- The major index generating function of standard Young tableaux of shapes of the form “staircase minus rectangle” 111122
- Convergence of random continued fractions 123134
- Tensor product decomposition of ̂𝔰𝔩(𝔫) modules and identities 131142
- Ramanujan, Robin, highly composite numbers, and the Riemann Hypothesis 145156
- A quaternionic proof of the representation formulas of two quaternary quadratic forms 157168
- Back Cover Back Cover1186