SIMPLE ZEROS OF L-FUNCTIONS AND THE WEYL-TYPE SUBCONVEXITY

Abstract

Let f be a self-dual primitive Maass or modular forms for level 4. For such a form f, we define N-f(8)(T):=|{rho is an element of C : |xi(rho)| <= T, rho is a non-trivial simple zero of Lf(8)}|. We establish an omega result for N-f(8)(T), which is N-f(8)(T) = Omega(T (1)(6) (c)) for any is an element of E > 0. For this purpose, we need to establish the Weyl-type subcon-vexity for L-functions attached to primitive Maass forms by following a recent work of Aggarwal, Holowinsky, Lin, and Qi.