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 ClK such that L(1/2, fK × chi) ≠ 0 and L(1/2, gK × chi) ≠ 0. The proof is based on a non-vanishing result for Fourier coefficients of Siegel modular forms combined with the theory of Yoshida liftings.
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