Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions

Abstract

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 chi of the ideal class group Cl_K such that L(1/2, f_K \times chi) \neq 0 and L(1/2, g_K \times chi) \neq 0. The proof is based on a non-vanishing result for Fourier coefficients of Siegel modular forms combined with the theory of Yoshida liftings.

23 pages, version after incorporating referee's comments; to appear in J. Lond. Math. Soc

References in corpus (1)

• Bessel models for lowest weight representations of GSp(4,R)

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• Dimension formulas for Siegel modular forms of level $4$
• Wide moments of $L$-functions I: Twists by class group characters of imaginary quadratic fields
• On counting cuspidal automorphic representations for $\mathrm{GSp}(4)$
• On fundamental Fourier coefficients of Siegel cusp forms of degree 2
• Non-vanishing of fundamental Fourier coefficients of paramodular forms
• A relation between multiplicity one and Bocherer's conjecture
• Algebraicity of $L$-values for ${\text{GSp}}_4\times {\text{GL}}_2$ and ${\text{GSp}}_4\times {\text{GL}}_2\times {\text{GL}}_2$
• Inner product formula for Yoshida lifts
• Invariant Vectors for Weak Endoscopic and Saito-Kurokawa Lifts to GSp(4)