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arXiv · 2101.04418

Correlations of sieve weights and distributions of zeros

Aled Walker
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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.

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Aled Walker. 2021-01-12. Correlations of sieve weights and distributions of zeros. https://arxiv.org/abs/2101.04418

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