Conductor zeta function for the GL(2) universal family

Abstract

We obtain a Weyl law with power savings for the universal families of cuspidal automorphic representations, ordered by analytic conductor, of ${\mathrm{GL}}_2$ over $\mathbb{Q}$, as well as for Hecke characters over any number field. The method proceeds by establishing the requisite analytic properties of the underlying conductor zeta function.

26 pages