A New Zero-Density Estimate for the Riemann Zeta Function close to the 1-line

3:00pm, Wednesday 15 October 2025

Abstract

In this talk we present a new type of zero-density estimate for the Riemann zeta function close to the one-line. In particular, we show that the number of zeros in this region remains bounded by an absolute constant when approaching the left edge of the Korobov-Vinogradov zero-free region. As a consequence, we obtain an essentially optimal refinement of a result due to Pintz concerning the error term in the prime number theorem.