An analogue of a formula of Popov
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.01759
- arXiv:
- arXiv:2408.01759
- Bibcode:
- 2024arXiv240801759R
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Classical Analysis and ODEs
- E-Print:
- V2: We have added a final section containing a proof of a generalization of the Ramanujan-Guinand formula