On the non-vanishing of modular $L$-values and fourier coefficients of
cusp forms
On the non-vanishing of modular $L$-values and fourier coefficients of
cusp forms
We prove a non-vanishing result of modular L-values with quadratic twists, where the quadratic discriminants are in a short interval. Using this fact and Waldspurger's theorem, we improve the results of Balog-Ono[The chebotarev density theorem in short intervals and some questions of Serre, Journal of number theory. 91(2):356-371(2001)] on the …