Fourier optimization and quadratic forms

Activity: Talk or presentationTalk at conference or symposiumScience to science


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.
PeriodAug 2022
Event titleElementare und Analytische Zahlentheorie - ELAZ 2022
Event typeConference
LocationPoznań, PolandShow on map
Degree of RecognitionInternational


  • Fourier analysis
  • quadratic forms
  • generalized riemann hypothesis