Simultaneous Non-vanishing of Twists

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( 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 mod...

Vanishing and Non-vanishing Dirichlet Twists of L-functions of Elliptic Curves Jack Fearnley, Hershy Kisilevsky, and Masato Kuwata

Let L(E/Q, s) be the L-function of an elliptic curve E defined over the rational field Q. We examine the vanishing and non-vanishing of the central values L(E, 1, χ) of the twisted L-function as χ ranges over Dirichlet characters of given order.

ON THE NON-VANISHING OF HECKE L-VALUES MODULO p

In this article, we follow Hida’s approach to establish an analogue of Washington’s theorem on the non-vanishing modulo p of Hecke L-values for CM fields with anticyclotomic twists

Non-vanishing of Quadratic Twists of Modular L-functions

Vanishing and non-vanishing Dirichlet twists of L-functions of elliptic curves

Let L(E/Q, s) be the L-function of an elliptic curve E defined over the rational field Q. We examine the vanishing and non-vanishing of the central values L(E, 1, χ) of the twisted L-function as χ ranges over Dirichlet characters of given order.