TY - CHAP

T1 - Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook

AU - Berndt, Bruce C.

AU - Lee, Yoonbok

AU - Sohn, Jaebum

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

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U2 - 10.1007/978-0-387-78510-3_2

DO - 10.1007/978-0-387-78510-3_2

M3 - Chapter

AN - SCOPUS:84859480694

SN - 9780387785097

T3 - Developments in Mathematics

SP - 21

EP - 42

BT - SURVEYS IN NUMBER THEORY

A2 - ALLADI, KRISHNASWAMI

ER -