Weighted divisor sums and Bessel function series, IV

Research output: Contribution to journalArticle

Abstract

One fragment (p. 335) published with Ramanujan's Lost Notebook contains two formulas, each involving a finite trigonometric sum and a doubly infinite series of Bessel functions. The identities are connected with the classical circle and divisor problems, respectively. This paper is devoted to the first identity. First, we obtain a generalization in the setting of Riesz sums. Second, we prove a trigonometric analogue.

Original languageEnglish (US)
Pages (from-to)79-102
Number of pages24
JournalRamanujan Journal
Volume29
Issue number1-3
DOIs
StatePublished - Nov 20 2012

Keywords

  • Bessel functions
  • Circle problem
  • Dirichlet L-series
  • Ramanujan's Lost Notebook
  • Riesz sums
  • Weighted divisor sums

ASJC Scopus subject areas

  • Algebra and Number Theory

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