Aled Walker
Published 2021-01-12Version 1
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.
A lower bound in an approximation problem involving the zeros of the Riemann zeta function
On a Lower Bound for $\|(4/3)^k\|$
Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
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