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arXiv · 2407.04554

A Ramanujan bound for Drinfeld modular forms

Sjoerd de Vries
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Abstract

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 an application, we deduce a Ramanujan bound on the traces of Hecke operators.

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Sjoerd de Vries. 2024-07-05. A Ramanujan bound for Drinfeld modular forms. https://doi.org/10.1093/imrn%2Frnaf193

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