Integrality of twisted L-values of elliptic curves

Wiersema, Hanneke; Wuthrich, Christian

Abstract

Under suitable, fairly weak hypotheses on an elliptic curve E/Q and a primitive non-trivial Dirichlet character χ, we show that the algebraic L-value L (E, χ) at s = 1 is an algebraic integer. For instance, for semistable curves L (E, χ) is integral whenever E admits no isogenies defined over Q.

Citation

Wiersema, H., & Wuthrich, C. (2022). Integrality of twisted L-values of elliptic curves. Documenta Mathematica, 27, 2041-2066. https://doi.org/10.25537/dm.2022v27.2041-2066

• Journal Article Type: Article
• Acceptance Date: Oct 24, 2022
• Online Publication Date: Dec 31, 2022
• Publication Date: Dec 31, 2022
• Deposit Date: Oct 25, 2022
• Publicly Available Date: Dec 31, 2022
• Journal: Documenta Mathematica
• Electronic ISSN: 1431-0643
• Publisher: Documenta Mathematica
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Pages: 2041-2066
• DOI: https://doi.org/10.25537/dm.2022v27.2041-2066
• Public URL: https://nottingham-repository.worktribe.com/output/4903750
• Publisher URL: https://elibm.org/?q=Integrality+of+twisted+L-values+of+elliptic+curves