Poisson summation formulas involving the sum-of-squares function

Nir Lev; Gilad Reti

doi:10.1007/s11856-021-2252-8

Poisson summation formulas involving the sum-of-squares function

Nir Lev, Gilad Reti

Department of Mathematics

Bar-Ilan University

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

Abstract

We obtain new Poisson type summation formulas with nodes ±n and with weights involving the function r_k(n) that gives the number of representations of a positive integer n as the sum of k squares. Our results extend summation formulas due to Guinand and Meyer that involve the sum-of-three-squares function r₃(n).

Original language	English
Pages (from-to)	403-421
Number of pages	19
Journal	Israel Journal of Mathematics
Volume	246
Issue number	1
DOIs	https://doi.org/10.1007/s11856-021-2252-8
State	Published - Dec 2021

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-021-2252-8

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title = "Poisson summation formulas involving the sum-of-squares function",

abstract = "We obtain new Poisson type summation formulas with nodes ±n and with weights involving the function rk(n) that gives the number of representations of a positive integer n as the sum of k squares. Our results extend summation formulas due to Guinand and Meyer that involve the sum-of-three-squares function r3(n).",

author = "Nir Lev and Gilad Reti",

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AU - Reti, Gilad

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AB - We obtain new Poisson type summation formulas with nodes ±n and with weights involving the function rk(n) that gives the number of representations of a positive integer n as the sum of k squares. Our results extend summation formulas due to Guinand and Meyer that involve the sum-of-three-squares function r3(n).

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U2 - 10.1007/s11856-021-2252-8

DO - 10.1007/s11856-021-2252-8

M3 - مقالة

SN - 0021-2172

VL - 246

SP - 403

EP - 421

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Poisson summation formulas involving the sum-of-squares function

Abstract

All Science Journal Classification (ASJC) codes

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