An integral of Dedekind eta-functions in Ramanujan's lost notebook

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Abstract

On page 207 in his lost notebook, Ramanujan recorded a curious formula for an integral of a certain quotient of Dedekind eta-functions. The formula involves a mysterious constant C, which Ramanujan claims, with two question marks appended, is a simple multiple of a Dirichlet L-function evaluated at the argument 2. The integral formula was first proved by S. H. Son, but he did not establish Ramanujan's formula for C. We give an entirely different proof of this result which also shows that Ramanujan's questioned formula for C is correct.

Original languageEnglish (US)
Pages (from-to)33-39
Number of pages7
JournalJournal fur die Reine und Angewandte Mathematik
Issue number551
StatePublished - Dec 1 2002

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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