Fourier optimization and prime gaps

TL;DR

This paper explores extremal Fourier analysis problems and their application to prime gaps, providing improved bounds on the largest prime gap assuming the Riemann hypothesis.

Contribution

It introduces new extremal Fourier analysis techniques that lead to tighter bounds on prime gaps under the Riemann hypothesis.

Findings

Improved bounds for prime gaps assuming the Riemann hypothesis.

New extremal Fourier analysis methods applied to number theory.

Enhanced understanding of the connection between Fourier analysis and prime distribution.

Abstract

We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann hypothesis.