A Voronoi–Oppenheim summation formula for totally real number fields

Debika Banerjee; Ehud Moshe Baruch; Evgeny Tenetov

doi:10.1016/j.jnt.2018.04.008

A Voronoi–Oppenheim summation formula for totally real number fields

Debika Banerjee, Ehud Moshe Baruch, Evgeny Tenetov

Mathematics

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

2 Scopus citations

Abstract

We obtain a Voronoi–Oppenheim summation formula for divisor functions of totally real number fields. This generalizes a formula proved by Oppenheim in 1927. We use a similar method to the one developed by Beineke and Bump in order to prove the classical Oppenheim summation using a certain Eisenstein series and representation theory. Our formula has a simple formulation for real quadratic number fields.

Original language	English
Pages (from-to)	63-97
Number of pages	35
Journal	Journal of Number Theory
Volume	199
DOIs	https://doi.org/10.1016/j.jnt.2018.04.008
State	Published - Jun 2019

Keywords

Bessel functions
Voronoi summation

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2018.04.008

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title = "A Voronoi–Oppenheim summation formula for totally real number fields",

abstract = "We obtain a Voronoi–Oppenheim summation formula for divisor functions of totally real number fields. This generalizes a formula proved by Oppenheim in 1927. We use a similar method to the one developed by Beineke and Bump in order to prove the classical Oppenheim summation using a certain Eisenstein series and representation theory. Our formula has a simple formulation for real quadratic number fields.",

keywords = "Bessel functions, Voronoi summation",

author = "Debika Banerjee and Baruch, {Ehud Moshe} and Evgeny Tenetov",

note = "Publisher Copyright: {\textcopyright} 2018",

year = "2019",

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AU - Banerjee, Debika

AU - Baruch, Ehud Moshe

AU - Tenetov, Evgeny

PY - 2019/6

Y1 - 2019/6

N2 - We obtain a Voronoi–Oppenheim summation formula for divisor functions of totally real number fields. This generalizes a formula proved by Oppenheim in 1927. We use a similar method to the one developed by Beineke and Bump in order to prove the classical Oppenheim summation using a certain Eisenstein series and representation theory. Our formula has a simple formulation for real quadratic number fields.

AB - We obtain a Voronoi–Oppenheim summation formula for divisor functions of totally real number fields. This generalizes a formula proved by Oppenheim in 1927. We use a similar method to the one developed by Beineke and Bump in order to prove the classical Oppenheim summation using a certain Eisenstein series and representation theory. Our formula has a simple formulation for real quadratic number fields.

KW - Bessel functions

KW - Voronoi summation

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AN - SCOPUS:85059446017

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SP - 63

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

A Voronoi–Oppenheim summation formula for totally real number fields

Abstract

Keywords

ASJC Scopus subject areas

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