Voronoi summation formula for Gaussian integers

Debika Banerjee, Ehud Moshe Baruch, Daniel Bump

Research output: Contribution to journalArticlepeer-review


We prove a Voronoi–Oppenheim summation formula for divisor functions associated with Gaussian integers. This formula is a direct generalization of Oppenheim’s summation formula for classical divisor functions. To prove the formula we construct an Eisenstein series and study its properties. Our method of proof is similar to Beineke and Bump’s proof of the classical Oppenheim summation formula.

Original languageEnglish
Pages (from-to)253-274
Number of pages22
JournalRamanujan Journal
Issue number1
StatePublished - Jan 2022


  • Bessel functions
  • Gaussian integers
  • Voronoi summation formula

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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