Journal of the Ramanujan Mathematical Society

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Base Change, Tensor Product and the Birch-Swinnerton-Dyer Conjecture


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1 Department of Mathematics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
     

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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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  • Base Change, Tensor Product and the Birch-Swinnerton-Dyer Conjecture

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Authors

Peng-Jie Wong
Department of Mathematics, Queen’s University, Kingston, Ontario K7L 3N6, Canada

Abstract


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.

References