An analogue of a formula of Popov
Number Theory
2024-08-14 v2 Classical Analysis and ODEs
Abstract
Let denote the number of representations of the positive integer as the sum of squares. We prove a new summation formula involving and the Bessel functions of the first kind, which constitutes an analogue of a result due to the Russian mathematician A. I. Popov.
Cite
@article{arxiv.2408.01759,
title = {An analogue of a formula of Popov},
author = {Pedro Ribeiro},
journal= {arXiv preprint arXiv:2408.01759},
year = {2024}
}
Comments
V2: We have added a final section containing a proof of a generalization of the Ramanujan-Guinand formula; Reference [13] of the previous version corrected