Determination of elliptic curves by their adjoint p-adic L-functions

Abstract

Fix p an odd prime. Let E be an elliptic curve over QQ with semistable reduction at p. We show that the adjoint p-adic L-function of E evaluated at infinitely many integers prime to p completely determines up to a quadratic twist the isogeny class of E . To do this, we prove a result on the determination of isobaric representations of GL(3,AQ)GL(3,AQ) by certain L-values of p-power twists.

Additional Information

© 2015 Elsevier Inc. Received 10 June 2014, Revised 20 October 2014, Accepted 2 December 2014, Available online 4 February 2015. Communicated by Ph. Michel. The author would like to thank her advisor Dinakar Ramakrishnan, Wenzhi Luo, Philippe Michel and Gergely Harcos for useful discussions. The author would also like to thank the referee for their comments which improved the presentation of this paper.

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