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2018 Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field
Ian Petrow
Algebra Number Theory 12(10): 2471-2498 (2018). DOI: 10.2140/ant.2018.12.2471

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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Ian Petrow. "Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field." Algebra Number Theory 12 (10) 2471 - 2498, 2018. https://doi.org/10.2140/ant.2018.12.2471

Information

Received: 6 May 2018; Revised: 22 July 2018; Accepted: 23 August 2018; Published: 2018
First available in Project Euclid: 14 February 2019

zbMATH: 07026824
MathSciNet: MR3911137
Digital Object Identifier: 10.2140/ant.2018.12.2471

Subjects:
Primary: 11F25
Secondary: 11F11, 11F72, 11G20, 14G15

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 10 • 2018
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