Ramanujan's lost notebook Part IV George E. Andrews, Bruce C. Berndt

Format:

Book

Author/Creator:

Andrews, George E., 1938-

Contributor:

Berndt, Bruce C., 1939-

Language:

English

Subjects (All):

Ramanujan Aiyangar, Srinivasa, 1887-1920.

Ramanujan Aiyangar, Srinivasa.

Mathematical analysis.

Number theory.

Mathematicians--India--Biography.

Mathematicians.

Mathematics.

India.

Number Theory.

Analysis.

Fourier Analysis.

Special Functions.

Medical Subjects:

Mathematics.

India.

Local Subjects:

Mathematics.

Number Theory.

Analysis.

Fourier Analysis.

Special Functions.

Genre:

Biographies

Physical Description:

1 online resource

Place of Publication:

New York Springer ©2013

Language Note:

English

System Details:

PDF

text file

Summary:

"In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the fourth of five volumes that the authors plan to write on Ramanujan's lost notebook. In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series. Most of the entries examined in this volume fall under the purviews of number theory and classical analysis. Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems."--Publisher's description

Contents:

1. Introduction

2. Double series of Bessel functions and the circle and divisor problems

3. Koshliakov's formula and Guinand's formula

4. Theorems featuring the gamma function

5. Hypergeometric series

6. Two partial manuscripts on Euler's constant y

7. Problems in diophantine approximation

8. Number theory

9. Divisor sums

10. Identities related to the Riemann zeta function and periodic zeta functions

11. Two partial unpublished manuscripts on sums involving primes

12. An unpublished manuscript of Ramanujan on infinite series identities

13. A partial manuscript on Fourier and Laplace transforms

14. Integral analogues of theta functions and Gauss sums

15. Functional equations for products of Mellin transforms

16. A preliminary version of Ramanujan's paper "On the product [mathematical equation]"

17. A preliminary version of Ramanujan's paper "On the integral [mathematical equation]"

18. A partial manuscript connected with Ramanujan's paper "Some definite integrals"

19. Miscellaneous results in analysis

20. Elementary results

21. A strange, enigmatic partial manuscript

Introduction Double Series of Bessel Functions and the Circle and Divisor Problems Koshliakov's Formula and Guinand's Formula Theorems Featuring the Gamma Function Hypergeometric Series Two Partial Manuscripts on Euler's Constant γ Problems in Diophantine Approximation Number Theory Divisor Sums Identities Related to the Riemann Zeta Function and Periodic Zeta Functions Two Partial Unpublished Manuscripts on Sums Involving Primes An Unpublished Manuscript of Ramanujan on Infinite Series Identities A Partial Manuscript on Fourier and Laplace Transforms Integral Analogues of Theta Functions and Gauss Sums Functional Equations for Products of Mellin Transforms A Preliminary Version of Ramanujan's Paper "On the Product πn=0[infinity][1+(xa+nd)3] " A Preliminary Version of Ramanujan's Paper "On the Integral [integral]x0tan-1ttdt " A Partial Manuscript Connected with Ramanujan's Paper "Some Definite Integrals" Miscellaneous Results in Analysis Elementary Results A Strange, Enigmatic Partial Manuscript

Notes:

Includes bibliographical references (pages 421-434) and index

Online resource; title from PDF title page (SpringerLink, viewed November 7, 2013)

Other Format:

Print version (multi-volume) Andrews, George E., 1938- Ramanujan's lost notebook

ISBN:

9781461440819

1461440815

1461440807

9781461440802

1322332711

9781322332710

OCLC:

847842072

Access Restriction:

Restricted for use by site license