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Publication . Article . Preprint . 2021

Poisson summation formulas involving the sum-of-squares function

Nir Lev; Gilad Reti;
Open Access
English
Abstract
We obtain new Poisson type summation formulas with nodes $\pm \sqrt{n}$ 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 $r_3(n)$.
To appear in Israel Journal of Mathematics
Subjects

Mathematics - Classical Analysis and ODEs, Mathematics - Functional Analysis, Mathematics - Number Theory, 11E25, 42B10, 52C23, Classical Analysis and ODEs (math.CA), Functional Analysis (math.FA), Number Theory (math.NT), FOS: Mathematics, General Mathematics

Related Organizations
18 references, page 1 of 2

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Funded by
EC| HARMONIC
Project
HARMONIC
Studies in Harmonic Analysis and Discrete Geometry: Tilings, Spectra and Quasicrystals
  • Funder: European Commission (EC)
  • Project Code: 713927
  • Funding stream: H2020 | ERC | ERC-STG
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