Simultaneous non-vanishing of quadratic Dirichlet L-functions and twists of Hecke L-functions

Twisted first moment of quadratic and quadratic twist $L$-functions

“…We note that the above result improves upon [18,Corollary 1.4]. Moreover, it is pointed out in [17] that the arguments used in the proof of [17,Theorem 1.1] can be extended to show that *…”

“…Instead of studying L-functions twisted by characters to a fixed modulus, one may also study L-functions twisted by characters to a fixed order. In [18], G. Maiti established a simultaneous non-vanishing result for quadratic Dirichlet L-functions and quadratic twists of modular L-functions. A key ingredient in his proof is an asymptotical formula on the first moment of central values of the product of a quadratic Dirichlet L-function and a quadratic twist of a modular L-function.…”