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Special values of L-functions and false Tate curve extensions.

Bouganis, A. (2010) 'Special values of L-functions and false Tate curve extensions.', Journal of the London Mathematical Society., 82 (3). pp. 596-620.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1112/jlms/jdq041
Publisher 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.
Date accepted:21 January 2010
Date deposited:11 April 2017
Date of first online publication:20 September 2010
Date first made open access:No date available

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