Congruences for the partition function

Abstract: The partition function p(n) counts the number of ways to break a natural number n into parts. The arithmetic properties of this function have been the topic of intensive study for many years. Much of the interest (and the difficulty) in this problem arises from the fact that values of the partition function are given by the coefficients of a weakly holomorphic modular form of half-integral weight. I’ll describe some recent work with Olivia Beckwith and Martin Raum, and with Patrick Allen and Shiang Tang which goes a long way towards explaining exactly when congruences for the partition function can occur. The main tools are techniques from the theory of modular forms, Galois representations, and analytic number theory.

number theory

Audience: researchers in the discipline

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11