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 χ of the ideal class group ClK such that L( 1 2 , fK × χ) 6= 0 and L( 1 2 , gK × χ) 6= 0. The proof is based on a non-vanishing result for Fourier coefficients of Siegel modular forms combined with the theory of Yoshida liftings.

DOI: 10.1112/jlms/jdt008

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Cite this paper

@article{Saha2013YoshidaLA, title={Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions}, author={Abhishek Saha and Ralf Schmidt}, journal={J. London Math. Society}, year={2013}, volume={88}, pages={251-270} }