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 Nsf(T):=|{ρ∈C:|ℑ(ρ)| ≤ T, ρis a non-trivial simple zero ofLf (s)}|. We establish an omega result for Nsf(T), which isN sf(T) = Ω(T16−ɛ) for any ɛ > 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.