Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook

Bruce C. Berndt, Yoonbok Lee, Jaebum Sohn

Research output: Chapter in Book/Report/Conference proceedingChapter

13 Citations (Scopus)

Abstract

On two pages in his lost notebook, Ramanujan recorded several theorems involving the modified Bessel function Kν (z). These include Koshliakov's formula and Guinand's formula, both connected with the functional equation of nonanalytic Eisenstein series, and both discovered by these authors several years after Ramanujan's death. Other formulas, including one by K. Soni and two particularly elegant new results, are also stated without proof by Ramanujan. In this paper, we prove all the formulas claimed by Ramanujan on these two pages and conclude with a survey of related results.

Original languageEnglish
Title of host publicationSURVEYS IN NUMBER THEORY
EditorsKRISHNASWAMI ALLADI
Pages21-42
Number of pages22
DOIs
Publication statusPublished - 2008 Dec 1

Publication series

NameDevelopments in Mathematics
Volume17
ISSN (Print)1389-2177

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook'. Together they form a unique fingerprint.

  • Cite this

    Berndt, B. C., Lee, Y., & Sohn, J. (2008). Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook. In KRISHNASWAMI. ALLADI (Ed.), SURVEYS IN NUMBER THEORY (pp. 21-42). (Developments in Mathematics; Vol. 17). https://doi.org/10.1007/978-0-387-78510-3_2