Special values of L-functions and false Tate curve extensions

Bouganis, A.

doi:10.1112/jlms/jdq041

Special values of L-functions and false Tate curve extensions

Bouganis, A.

Authors

Professor Athanasios Bouganis athanasios.bouganis@durham.ac.uk
Professor

Abstract

In this paper we show how the p-adic Rankin–Selberg product construction of Hida can be combined with freeness results of Hecke modules of Wiles to establish interesting congruences between particular special values of L-functions of elliptic curves. These congruences are part of some deep conjectural congruences that follow from the work of Kato on the non-commutative Iwasawa theory of the false Tate curve extension. In the appendix by Vladimir Dokchitser it is shown that these congruences, combined with results from Iwasawa theory for elliptic curves, give interesting results for the arithmetic of elliptic curves over non-abelian extensions.

Citation

Bouganis, A. (2010). Special values of L-functions and false Tate curve extensions. Journal of the London Mathematical Society, 82(3), 596-620. https://doi.org/10.1112/jlms/jdq041

Journal Article Type	Article
Acceptance Date	Jan 21, 2010
Online Publication Date	Sep 20, 2010
Publication Date	Sep 20, 2010
Deposit Date	Sep 18, 2013
Publicly Available Date	Apr 11, 2017
Journal	Journal of the London Mathematical Society
Print ISSN	0024-6107
Electronic ISSN	1469-7750
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	82
Issue	3
Pages	596-620
DOI	https://doi.org/10.1112/jlms/jdq041

Files

Accepted Journal Article (329 Kb)
PDF

Copyright Statement
This is the accepted version of the following article: Bouganis, A. (2010). Special values of L-functions and false Tate curve extensions. Journal of the London Mathematical Society 82(3): 596-620 which has been published in final form at https://doi.org/10.1112/jlms/jdq041. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.