Journal of the Ramanujan Mathematical Society

Volume 33, Issue 1, March 2018 pp. 99–109.

Base change, tensor product and the Birch-Swinnerton-Dyer conjecture

Authors: Peng-Jie Wong
Author institution:Department of Mathematics, Queen's University, Kingston, Ontario K7L 3N6, Canada

Summary: We prove the Rankin-Selberg convolution of two cuspidal automorphic representations are automorphic whenever one of them arises from an irreducible representation of an abelian-by-nilpotent Galois extension, which extends the previous result of Arthur-Clozel. Moreover, if one of such representations is of dimension at most 2 and another representation arises from a nearly nilpotent extension or a Galois extension of degree at most 59, the automorphy of the Rankin-Selberg convolution has been derived. As an application, we show that certain quotients of L-functions associated to non-CM elliptic curves are automorphic, which generalises a result of M. R. Murty and V. K. Murty.

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