Zero density of L-functions related to Maass forms

Abstract

Let f(z) be a Hecke-Maass cusp form for SL2(ℤ), and let L(s, f) be the corresponding automorphic L-function associated to f. For sufficiently large T, let N(σ, T) be the number of zeros ρ = β +iγ of L(s, f) with |γ| ⩽ T, β ⩾ σ, the zeros being counted according to multiplicity. In this paper, we get that for 3/4 ⩽ σ ⩽ 1 − ɛ, there exists a constant C = C(ɛ) such that N(σ,T) ≪ T2(1−σ)/σ(logT)C, which improves the previous results.