Low lying zeros of Artin -functions

Abstract

We study the one-level density of Artin -functions twisted by a cuspidal automorphic representation under the strong Artin conjecture and certain conjectures on counting number fields. Our result is unconditional for -fields. For a non-self dual , it agrees with the unitary type . For a self-dual whose symmetric square -function has a pole at , it agrees with the symplectic type . For a self-dual whose exterior square -function has a pole at , the possible symmetry types are , , or . When , for cubic fields and quartic fields, we rediscover Yang's one-level density result in his thesis (Yang 2009). In the last section, we compute the one-level density of several families of Artin -functions arising from parametric polynomials