An exponentially averaged Vasyunin formula
Number Theory
2020-04-22 v1
Abstract
We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as a reciprocity formula for cotangent sums, related to the ones proven in [BC13], [ABB17].
Cite
@article{arxiv.2004.10086,
title = {An exponentially averaged Vasyunin formula},
author = {Sébastien Darses and Erwan Hillion},
journal= {arXiv preprint arXiv:2004.10086},
year = {2020}
}
Comments
This paper has been written from results already stated in a previous version of another paper in 2018, but has been now submitted separately. arXiv admin note: text overlap with arXiv:1805.06733