Hilbert Modular Forms and the Ramanujan Conjecture

Abstract

This paper completes the proof of the Ramanujan Conjecture for holomorphic Hilbert modular forms whose weights are all congruent modulo 2. As a consequence, the Weight-Monodromy Conjecture and the zeta function conjecture of Langlands are verified for all Quaternionic Shimura varieties.

28 pages