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

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.