Ramanujan's Lost Notebook, 1st Edition

  • Published By:
  • ISBN-10: 1461440815
  • ISBN-13: 9781461440819
  • DDC: 515
  • Grade Level Range: College Freshman - College Senior
  • 439 Pages | eBook
  • Original Copyright 2013 | Published/Released May 2014
  • This publication's content originally published in print form: 2013

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​​​​In 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 been deemed the mathematical equivalent of finding Beethoven's 10th symphony.This volume is the 4th of 5 planned volumes on Ramanujan's lost notebook.​ Unlike the first 3 books, the 4th book does not focus on q-series. Most 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 partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory.  Most 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. Review of the 2nd volume: "Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."- MathSciNet. Review of the first volume: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."- Gazette of the Australian Mathematical Society​

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
Other Frontmatter.
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 γ.
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”.
17: A Preliminary Version of Ramanujan's Paper “On the Integral”.
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.
Location Guide.