Yoshida lifts and simultaneous non‐vanishing of dihedral twists of modular L‐functions
Yoshida lifts and simultaneous non‐vanishing of dihedral twists of modular L‐functions
复制标题
吉田提升和模 L 函数二面扭曲的同时不消失
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Ralf Schmidt
中科院分区：
文献类型：
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作者：
A. Saha;Ralf Schmidt
给出椭圆模形f和g的权和阶满足一定条件，证明了理想类群CLk存在无穷多个虚二次域K和特征标χ，使得L(1/2，BCK(F)×χ)≠0和L(1/2，BCK(G)×χ)≠0).证明基于Siegel模形式的傅立叶系数的一个非零化结果，并结合吉田提升理论。
Given elliptic modular forms f and g satisfying certain conditions on their weights and levels, we prove (a quantitative version of the statement) that there exist infinitely many imaginary quadratic fields K and characters χ of the ideal class group ClK such that L(½, BCK(f) × χ) ≠ 0 and L(½, BCK(g) × χ) ≠ 0. The proof is based on a non‐vanishing result for Fourier coefficients of Siegel modular forms combined with the theory of Yoshida liftings.