English

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

R2 v1 2026-06-23T15:00:07.496Z