The Riemann zeta function and exact exponential sum identities of divisor functions
Number Theory
2023-11-15 v1
Abstract
We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existence of infinite families of exact exponential sum identities involving the divisor functions, and we provide examples of these identities. We conjecturally propose a method to compute divisor functions by matrix inversion, without employing arithmetic techniques.
Keywords
Cite
@article{arxiv.2311.07657,
title = {The Riemann zeta function and exact exponential sum identities of divisor functions},
author = {Maria Nastasescu and Nicolas Robles and Bogdan Stoica and Alexandru Zaharescu},
journal= {arXiv preprint arXiv:2311.07657},
year = {2023}
}
Comments
24 pages, 2 figures