An analogue of a formula of Popov

2024/08/03 by Ribeiro, Pedro
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.01759

Abstract

Let r_k(n) denote the number of representations of the positive integer n as the sum of k squares. We prove a new summation formula involving r_k(n) and the Bessel functions of the first kind, which constitutes an analogue of a result due to the Russian mathematician A. I. Popov.

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