Zero density for automorphic L-functions

In this paper, zero density estimates for automorphic L-functions L(s,π) for GLn are deduced from a bound for an integral power moment of L(s,π) on the critical line Re(s)=1/2. 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 SL2(Z), bounds for zero density for L(s,g) in short strips are proved, which extend Ivićʼs results on long strips. For a self-dual Hecke Maass eigenform f for SL3(Z), estimates of zero density for L(s,f) 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 L(1/2+it,π), the Rankin-Selberg theory, and the Halász-Montgomery-Jutila method.