Linear properties of zeros of the Riemann zeta function

Description:

This project aims to establish upper and lower bounds for counts of zeros of the Riemann zeta and Dirichlet L-functions in Bohr sets. A combination of techniques to estimate mean values of Dirichlet polynomials over Bohr sets with the method of moments/mollifiers has the potential to go beyond results which follow from an application of the Guinand-Weil explicit formula. This opens avenues to apply ideas from combinatorics with the goal of understanding additive properties of the zeros and is important from the perspective of oscillation theorems.