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

Details 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

2011-09-28

arxiv.org/abs/1109.6192v2

Mathematics

Number Theory

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Scientific paper

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.

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