Fourier optimization and quadratic forms

Description

Abstract:
The study of integers and primes represented by binary quadratic forms is a classical problem, going back to Fermat. We will discuss a Fourier analysis approach to this problem, based on joint work with Andrés Chirre. For a given form and integer l>2, this approach gives us strong estimates for the average number of representations of integers that are multiples of l. This leads to unconditional upper bounds on the number of primes in short intervals represented by a given form, and, conditionally on the generalized Riemann hypothesis, an upper bound on the maximum gap between such consecutive primes. The latter extends a method of Carneiro, Milinovich, and Soundararajan.

Period	Aug 2022
Event title	Elementare und Analytische Zahlentheorie - ELAZ 2022
Event type	Conference
Location	Poznań, PolandShow on map
Degree of Recognition	International