English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Extremal primes for elliptic curves without complex multiplication

MPS-Authors
/persons/resource/persons246184

Turnage-Butterbaugh,  Caroline LaRoche
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

1807.05255.pdf
(Preprint), 199KB

Supplementary Material (public)
There is no public supplementary material available
Citation

David, C., Gafni, A., Malik, A., Prabhu, N., & Turnage-Butterbaugh, C. L. (2020). Extremal primes for elliptic curves without complex multiplication. Proceedings of the American Mathematical Society, 148(3), 929-943. doi:10.1090/proc/14748.


Cite as: https://hdl.handle.net/21.11116/0000-0005-E509-F
Abstract
Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to the Hasse bound. Assuming that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis, we give the first non-trivial upper bounds for the number of such primes when E is a curve without complex multiplication. In order to obtain this bound, we use explicit equidistribution for the Sato-Tate measure as in the work of Rouse and Thorner (arXiv:1305.5283) and refine certain intermediate estimates taking advantage of the fact that extremal primes have a very small Sato-Tate measure.