Voronoi summation formula for Gaussian integers
type: Item
instance of: scholarly article
title: Voronoi summation formula for Gaussian integers
zbMATH Open document ID: 1497.11196
author: Debika Banerjee
author: Ehud Moshe Baruch
author: Daniel Bump
published in: The Ramanujan Journal
publication date: 2022-01-24T00:00:00Z
review text: In the paper under review, the authors state the Voronoi-Oppenheim summation formula for Gaussian integers \(\mathbb{Z}[i ]\) in case of smooth compactly supported function on \(\mathbb{C}^\times\) and as a limiting case they get Voronoi summation formula for \(\mathbb{Z}[i ]\). Their method of proof follows closely the method of \textit{J. Beineke} and \textit{D. Bump} [Forum Math. 18, No. 6, 869--906 (2006; Zbl 1206.11120)].
reviewed by: Sami Omar
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 7462098
zbMATH Keywords: Bessel functions
zbMATH Keywords: Gaussian integers
zbMATH Keywords: Voronoi summation formula
MaRDI profile type: Publication
full work available at URL: s11139-020-00378-4
OpenAlex ID: W3159163294
cites work: On the Voronoĭ formula for GL(n)
cites work: Moments of the Riemann zeta function and Eisenstein series. I
cites work: A summation formula for divisor functions associated to lattices
cites work: A kernel formula for the action of the Weyl element in the Kirillov model of \(\mathrm{SL}(2,\mathbb{C})\)
cites work: Bessel identities in the Waldspurger correspondence over the real numbers
cites work: A note on the mean value of the zeta and \(L\)-functions. XIII.
cites work: Q3996745
cites work: Q4368847
cites work: Q3999351
cites work: Q4275389
cites work: Voronoi formulas on GL(n)
cites work: The Voronoi formula and double Dirichlet series
cites work: Q4298518
cites work: Automorphic distributions, \(L\)-functions, and Voronoi summation for \(\text{GL}(3)\)
cites work: A general Voronoi summation formula for GL(n,Z)
cites work: Voronoi summation formulae on \(\mathrm{GL}(n)\)
DOI: 10.1007/S11139-020-00378-4
description: scientific article; zbMATH DE number 7462098