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arXiv · 2408.01759

An analogue of a formula of Popov

Pedro Ribeiro
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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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Pedro Ribeiro. 2024-08-03. An analogue of a formula of Popov. https://arxiv.org/abs/2408.01759

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