Monotone chains of Hecke cusp forms

Abstract: We discuss a general joint equidistribution result for the Fourier coefficients of Hecke cusp forms. One simple consequence of such a result is that there exist infinitely many integers n (in fact an upper density of this set is positive) such that $\tau (n)<\tau (n+1)<\tau(n+2)$ where $\tau$ is a Ramanujan $\tau$-function. This is based on a joint work with A. Mangerel (CRM).

number theory

Audience: researchers in the topic

Warsaw Number Theory Seminar