Representations attached to elliptic curves with a non-trivial odd torsion point
Number Theory
2022-10-18 v2
Abstract
We give a classification of the cuspidal automorphic representations attached to rational elliptic curves with a non-trivial torsion point of odd order. Such elliptic curves are parameterizable, and in this paper, we find the necessary and sufficient conditions on the parameters to determine when split or non-split multiplicative reduction occurs. Using this and the known results on when additive reduction occurs for these parametrized curves, we classify the automorphic representations in terms of the parameters.
Keywords
Cite
@article{arxiv.2106.15722,
title = {Representations attached to elliptic curves with a non-trivial odd torsion point},
author = {Alexander J. Barrios and Manami Roy},
journal= {arXiv preprint arXiv:2106.15722},
year = {2022}
}
Comments
17 pages; incorporates referee's suggestions; a small correction to the statement of Theorem 3.3; final version to appear in Bulletin of the London Mathematical Society