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arXiv · 1710.09869

Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field

Ian Petrow
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Abstract

We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applications to the analytic theory of elliptic curves over a finite field, going beyond the Riemann hypothesis over finite fields. As the main tool to prove our bound on traces of Hecke operators, we develop a Petersson formula for newforms for general nebentype characters.

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BibTeXRIS

Ian Petrow. 2018-08-23. Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field. https://doi.org/10.2140/ant.2018.12.2471

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