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Hilbert Modular Forms and the Ramanujan Conjecture

Don Blasius
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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.

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Don Blasius. 2005-11-01. Hilbert Modular Forms and the Ramanujan Conjecture. https://arxiv.org/abs/math/0511007

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