Zero density for automorphic L-functions.

Abstract: In this paper, zero density estimates for automorphic L-functions for are deduced from a bound for an integral power moment of on the critical line . In particular for the Riemann zeta function, classical zero density estimates are extended to short vertical strips. For g being a holomorphic or Maass eigenform for , bounds for zero density for in short strips are proved, which extend Ivićʼs results on long strips. For a self-dual Hecke Maass eigenform f for , estimates of zero density for in short and long strips are also proved. The proofs use a zero detecting argument, a large sieve inequality, a bound for an integral power moment of , the Rankin–Selberg theory, and the Halász–Montgomery–Jutila method. [Copyright &y& Elsevier]