Non-abelian congruences between special values of L-functions of elliptic curves; the CM case

Bouganis, A.

Abstract

In this work we prove congruences between special values of L-functions of elliptic curves with CM that seem to play a central role in the analytic side of the non-commutative Iwasawa theory. These congruences are the analog for elliptic curves with CM of those proved by Kato, Ritter and Weiss for the Tate motive. The proof is based on the fact that the critical values of elliptic curves with CM, or what amounts to the same, the critical values of Grössencharacters, can be expressed as values of Hilbert–Eisenstein series at CM points. We believe that our strategy can be generalized to provide congruences for a large class of L-values.

Citation

Bouganis, A. (2011). Non-abelian congruences between special values of L-functions of elliptic curves; the CM case. International Journal of Number Theory, 07(07), 1883-1934. https://doi.org/10.1142/s179304211100468x

• Journal Article Type: Article
• Acceptance Date: Feb 14, 2011
• Publication Date: Nov 1, 2011
• Deposit Date: Sep 18, 2013
• Publicly Available Date: Apr 12, 2017
• Journal: International Journal of Number Theory
• Print ISSN: 1793-0421
• Electronic ISSN: 1793-7310
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 07
• Issue: 07
• Pages: 1883-1934
• DOI: https://doi.org/10.1142/s179304211100468x
• Public URL: https://durham-repository.worktribe.com/output/1447056