Weighted divisor sums and bessel function series. III

Research output: Contribution to journalArticlepeer-review

Abstract

On page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. The two identities are intimately connected with the classical circle and divisor problems, respectively. For each of Ramanujan's identities, there are three possible interpretations for the double series. In two earlier papers, the authors proved the two identities under each of two possible interpretations.Weighted (or twisted) divisor sums are central to the proofs. The ideas that the authors used in the second paper are extended here to derive analogous Bessel series identities for finite sums of products of two trigonometric (sine-sine, cosine-cosine, sine- cosine) functions.

Original languageEnglish (US)
Pages (from-to)67-96
Number of pages30
JournalJournal fur die Reine und Angewandte Mathematik
Issue number683
DOIs
StatePublished - Oct 2013

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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