Yoshida lifts and the Bloch-Kato conjecture for the convolution L-function

JOURNAL OF NUMBER THEORY

卷:133

Article

Agarwal, Mahesh¹  Klosin, Krzysztof² 

[1] Univ Michigan, Dept Math & Stat, Dearborn, MI 48128 USA

[2] CUNY Queens Coll, Dept Math, Flushing, NY 11367 USA

关键词: Congruences among automorphic forms;    Siegel modular forms;    Special L-values;    Galois representations;    Bloch-Kato conjecture;   

DOI  :  10.1016/j.jnt.2013.01.009

来源: Elsevier

【 摘 要 】

Let f(1) (resp. f(2)) denote two (elliptic) newforms of prime level N, trivial character and weight 2 (resp. k + 2, where k is an element of {8,12}). We provide evidence for the Bloch-Kato conjecture for the motive M = rho(f1) circle times rho(f2)(-k/2 - 1) by proving that under some assumptions the l-valuation of the order of the Bloch-Kato Selmer group of M is bounded from below by the l-valuation of the relevant L-value (a special value of the convolution L-function of f(1) and f(2)). We achieve this by constructing congruences between the Yoshida lift Y(f(1) circle times f(2)) of f(1) and f(2) and Siegel modular forms whose l-adic Galois representations are irreducible. Our result is conditional upon a conjectural formula for the Petersson norm of Y(f(1) circle times f(2)). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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