Ramanujan's lost notebook / George E. Andrews and Bruce C. Berndt.

Part IV

Includes bibliographical references and index.

Preface.- 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 Euler's Constant.-
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11 Two Partial Unpublished Manuscripts on Sums Involving Primes.-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 Infinite Series.-
13 A Partial Manuscript on Fourier and Laplace Transforms.-
14 Integral Analogues of Theta Functions adn Gauss Sums.-
15 Functional Equations for Products of Mellin Transforms.-
16 Infinite Products.-
17 A Preliminary Version of Ramanujan's Paper, On the Integral _0^x tan^(-1)t)/t dt.-
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.-
Provenance.-
References.-
Index.

"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.