A Voronoi-Oppenheim summation formula for totally real number fields
type: Item
instance of: scholarly article
title: A Voronoi-Oppenheim summation formula for totally real number fields
zbMATH Open document ID: 1425.11185
author: Debika Banerjee
author: Ehud Moshe Baruch
author: Evgeny Tenetov
published in: Journal of Number Theory
publication date: 2019-02-28T00:00:00Z
review text: The authors obtain a Voronoi-Oppenheim summation formula for divisor functions of totally real number fields. This generalizes a formula proved by \textit{A. Oppenheim} [Proc. Lond. Math. Soc. (2) 26, 295--350 (1927; JFM 53.0150.02)]. The method is similar to the one developed by \textit{J. Beineke} and \textit{D. Bump} [J. Number Theory 105, No. 1, 150--174 (2004; Zbl 1079.11041)] in order to prove the classical Oppenheim summation using a certain Eisenstein series and representation theory. The new formula has a simple formulation for real quadratic number fields.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 11R80
Mathematics Subject Classification ID: 11N99
Mathematics Subject Classification ID: 22E35
zbMATH DE Number: 7030975
zbMATH Keywords: Voronoi summation formula
zbMATH Keywords: Bessel functions
zbMATH Keywords: divisor functions
zbMATH Keywords: totally real number fields
MaRDI profile type: Publication
full work available at URL: j.jnt.2018.04.008
OpenAlex ID: W2807643787
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DOI: 10.1016/J.JNT.2018.04.008
description: scientific article; zbMATH DE number 7030975