Description
Book SynopsisIts 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.
Table of ContentsPreface.- 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9 Divisor Sums.- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions.- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series.- 13 A Partial Manuscript on Fourier and Laplace Transforms.- 14 Integral Analogues of Theta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.
