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.
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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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