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A Ramanujan bound for Drinfeld modular forms (2407.04554v1)
Published 5 Jul 2024 in math.NT and math.AG
Abstract: In this paper, we prove a Lefschetz trace formula for B\"ockle-Pink crystals on tame Deligne-Mumford stacks of finite type over $\mathbb{F}_q$ and apply it to the crystal associated to the universal Drinfeld module. Combined with the Eichler-Shimura theory developed by B\"ockle, this leads to a trace formula for Hecke operators on Drinfeld modular forms. As a corollary, we deduce a Ramanujan bound on the traces of Hecke operators.