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

Petrow, I; (2019) Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field. Algebra & Number Theory , 12 (10) pp. 2471-2498. 10.2140/ant.2018.12.2471. Green open access

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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.

Type: Article
Title: Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field
Open access status: An open access version is available from UCL Discovery
DOI: 10.2140/ant.2018.12.2471
Publisher version: https://doi.org/10.2140/ant.2018.12.2471
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10084829
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