Mass Equidistribution for Automorphic Forms of Cohomological Type on GL_2

Simon Marshall

Published 2010-06-16, updated 2010-08-13Version 2

We extend Holowinsky and Soundararajan's proof of quantum unique ergodicity for holomorphic Hecke modular forms on SL(2,Z), by establishing it for automorphic forms of cohomological type on GL_2 over an arbitrary number field which satisfy the Ramanujan bounds. In particular, we have uncondtional theorems over totally real and imaginary quadratic fields. In the totally real case we show that our result implies the equidistribution of the zero divisors of holomorphic Hecke modular forms, generalising a result of Rudnick over Q.