Correlations of sieve weights and distributions of zeros
Number Theory
2022-05-09 v2
Abstract
In this note we give two small results concerning the correlations of the Selberg sieve weights. We then use these estimates to derive a new (conditional) lower bound on the variance of the primes in short intervals, and also on the so-called `form factor' for the pair correlations of the zeros of the Riemann zeta function. Our bounds ultimately rely on the estimates of Bettin--Chandee for trilinear Kloosterman fractions.
Keywords
Cite
@article{arxiv.2101.04418,
title = {Correlations of sieve weights and distributions of zeros},
author = {Aled Walker},
journal= {arXiv preprint arXiv:2101.04418},
year = {2022}
}
Comments
Correction to some exponents