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). pp. 1883-1934.
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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1142/S179304211100468X|
|Publisher statement:||Electronic version of an article published as International Journal of Number Theory 07, 07, 2011, 1883-1934, 10.1142/S179304211100468X © copyright World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/ijnt|
|Date accepted:||14 February 2011|
|Date deposited:||12 April 2017|
|Date of first online publication:||November 2011|
|Date first made open access:||No date available|
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