Voronoi summation formula for Gaussian integers

Debika Banerjee; Ehud Moshe Baruch; Daniel Bump

doi:10.1007/s11139-020-00378-4

Voronoi summation formula for Gaussian integers

Debika Banerjee, Ehud Moshe Baruch, Daniel Bump

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 language	English
Pages (from-to)	253-274
Number of pages	22
Journal	Ramanujan Journal
Volume	57
Issue number	1
DOIs	https://doi.org/10.1007/s11139-020-00378-4
State	Published - Jan 2022

Keywords

Bessel functions
Gaussian integers
Voronoi summation formula

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s11139-020-00378-4

Cite this

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abstract = "We prove a Voronoi–Oppenheim summation formula for divisor functions associated with Gaussian integers. This formula is a direct generalization of Oppenheim{\textquoteright}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{\textquoteright}s proof of the classical Oppenheim summation formula.",

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KW - Gaussian integers

KW - Voronoi summation formula

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Voronoi summation formula for Gaussian integers

Abstract

Keywords

ASJC Scopus subject areas

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