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arXiv:1710.09869 [math.NT]AbstractReferencesReviewsResources

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

Ian Petrow

Published 2017-10-26Version 1

We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to a congruence subgroup. 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.

Categories: math.NT, cs.IT, math.IT
Subjects: 11F11, 11F25, 11G20, 11T71
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