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

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

3 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.

Funding

Research supported by ISF Grant No. 227/17 and ERC Starting Grant No. 713927.

Funders	Funder number
Horizon 2020 Framework Programme	713927
European Commission
Israel Science Foundation	227/17

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10.1007/s11856-021-2252-8

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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).",

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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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Poisson summation formulas involving the sum-of-squares function

Abstract

Bibliographical note

Funding

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