On Berndt's summation formula
Number Theory
2026-03-24 v2
Abstract
We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the Mntz formula and the Poisson summation formula. By utilizing known properties of Mellin inversion, we give an example from a discontinuous function. Several new applications are offered as corollaries.
Cite
@article{arxiv.2111.06256,
title = {On Berndt's summation formula},
author = {Alexander E. Patkowski},
journal= {arXiv preprint arXiv:2111.06256},
year = {2026}
}
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