Ebook: The Mathematical Legacy of Srinivasa Ramanujan

Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work still has an impact on many different fields of mathematical research. This book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.

Srinivasa Ramanujan was a mathematician brilliant beyond compare. There is extensive literature available on the work of Ramanujan, but what is more difficult to find in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by G. H. Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work is still having an impact on many different fields of mathematical research. The book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors, focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.

Srinivasa Ramanujan was a mathematician brilliant beyond compare. There is extensive literature available on the work of Ramanujan, but what is more difficult to find in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by G. H. Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work is still having an impact on many different fields of mathematical research. The book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors, focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.

Content:
Front Matter....Pages I-XI
The Legacy of Srinivasa Ramanujan....Pages 1-10
The Ramanujan ?-Function....Pages 11-23
Ramanujan’s Conjecture and ?-Adic Representations....Pages 25-37
The Ramanujan Conjecture from GL(2) to GL(n)....Pages 39-66
The Circle Method....Pages 67-96
Ramanujan and Transcendence....Pages 97-107
Arithmetic of the Partition Function....Pages 109-117
Some Nonlinear Identities for Divisor Functions....Pages 119-127
Mock Theta Functions and Mock Modular Forms....Pages 129-134
Prime Numbers and Highly Composite Numbers....Pages 135-147
Probabilistic Number Theory....Pages 149-153
The Sato–Tate Conjecture for the Ramanujan ?-Function....Pages 155-171
Erratum to: The Ramanujan ?-Function....Pages E1-E1
Back Matter....Pages 173-184

Srinivasa Ramanujan was a mathematician brilliant beyond compare. There is extensive literature available on the work of Ramanujan, but what is more difficult to find in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by G. H. Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work is still having an impact on many different fields of mathematical research. The book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors, focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.

Content:
Front Matter....Pages I-XI
The Legacy of Srinivasa Ramanujan....Pages 1-10
The Ramanujan ?-Function....Pages 11-23
Ramanujan’s Conjecture and ?-Adic Representations....Pages 25-37
The Ramanujan Conjecture from GL(2) to GL(n)....Pages 39-66
The Circle Method....Pages 67-96
Ramanujan and Transcendence....Pages 97-107
Arithmetic of the Partition Function....Pages 109-117
Some Nonlinear Identities for Divisor Functions....Pages 119-127
Mock Theta Functions and Mock Modular Forms....Pages 129-134
Prime Numbers and Highly Composite Numbers....Pages 135-147
Probabilistic Number Theory....Pages 149-153
The Sato–Tate Conjecture for the Ramanujan ?-Function....Pages 155-171
Erratum to: The Ramanujan ?-Function....Pages E1-E1
Back Matter....Pages 173-184
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