The Chebotarev density theorem and the pair correlation conjecture
In this note, we formulate pair correlation conjectures and refine the effective version of the Chebotarev density theorem established by the first two authors. Also, we apply our result to study Artin's primitive root conjecture and the Lang Trotter conjectures and obtain shaper error terms. 2010 Mathematics Subject Classification: 11M26, 11N45, 11R44.