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

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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• Algebra & Number Theory - View
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• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF
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