Simultaneous nonvanishing of products of L-functions associated to elliptic cusp forms

A generalized Riemann hypothesis states that all zeros of the completed Hecke L-function L⁎(f,s) of a normalized Hecke eigenform f on the full modular group should lie on the vertical line Re(s)=k2. It was shown in [6] that there exists a Hecke eigenform f of weight k such that L⁎(f,s)≠0 for sufficiently large k and any point on the line segments Im(s)=t0,k−12更多