Zero density of L-functions related to Maass forms

摘要

Let f(z) be a Hecke-Maass cusp form for SL_2(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 - ε, there exists a constant C = C(ε) such that N(σ, T) ＜ T~（2(1-σ)/σ）(logT)~C, which improves the previous results.