Logarithmic means and double series of Bessel functions

Bruce C. Berndt, Sun Kim

Research output: Contribution to journalArticlepeer-review


In his lost notebook, Ramanujan recorded two identities involving double series of Bessel functions that are closely connected with the classical, unsolved circle and divisor problems. In a series of papers with Zaharescu, the authors proved these identities under various interpretations, as well as Riesz mean analogues. In this paper, logarithmic mean analogues, also involving double series of Bessel functions, are established. Weighted divisor sums involving characters play a central role.

Original languageEnglish (US)
Pages (from-to)1535-1556
Number of pages22
JournalInternational Journal of Number Theory
Issue number5
StatePublished - Aug 5 2015


  • Bessel functions
  • Dirichlet L-functions
  • Dirichlet characters
  • Logarithmic mean
  • Ramanujan's lost notebook
  • weighted divisor sums

ASJC Scopus subject areas

  • Algebra and Number Theory


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