Primes in arithmetic progressions (in function fields)

3:00pm, Wednesday, 27th September

Abstract

Number theorists have long been interested in questions regarding the distribution of prime numbers. An important example of this is Dirichlet’s Theorem, which states that for any co-prime integers A and B, there are infinitely many primes congruent to A modulo B. But even stronger than this, asymptotic formulas have been found for the number of primes in such an arithmetic progression. In this talk we will start by giving a brief overview of what is known regarding the distribution of primes in arithmetic progressions, and then discuss similar problems but regarding irreducible polynomials over finite fields. We will highlight some recent breakthroughs of Sawin and Shusterman, and discuss a few ways in which we can build upon their work.