Nina Zubrilina (Princeton University): Convergence to Plancherel measure of Hecke eigenvalues

Abstract: Joint work with Peter Sarnak. We give rates, uniform in the degrees of test polynomials, of convergence of Hecke eigenvalues to the $p$-adic Plancherel measure. We apply this to the question of eigenvalue tuple multiplicity and to a question of Serre concerning the factorization of the Jacobian of the modular curve $X_0(N)$.

The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.