On a conjecture of Montgomery and Soundararajan
Number Theory
2020-09-15 v1
Abstract
We establish lower bounds for all weighted even moments of primes up to in intervals which are in agreement with a conjecture of Montgomery and Soundararajan. Our bounds hold unconditionally for an unbounded set of values of , and hold for all under the Riemann Hypothesis. We also deduce new unconditional -results for the classical prime counting function.
Keywords
Cite
@article{arxiv.2009.05760,
title = {On a conjecture of Montgomery and Soundararajan},
author = {Régis de la Bretèche and Daniel Fiorilli},
journal= {arXiv preprint arXiv:2009.05760},
year = {2020}
}
Comments
15 pages