Poisson summation formulas involving the sum-of-squares function

2020/02/06 by Nir Lev, Lev, Nir, Gilad Reti +1
Computer Science · Mathematics · #11E25 #42B10 #52C23 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Blind Source Separation Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2002.02324

openalex publication_date 2020/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

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