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Journal of the Ramanujan Mathematical Society

Volume 33, Issue 4, December 2018  pp. 399–426.

The Chebotarev density theorem and the pair correlation conjecture

Authors:  M. Ram Murty, V. Kumar Murty and Peng-Jie Wong
Author institution:Department of Mathematics and Statistics, Queen's University, Kingston, Ontario K7L 3N6, Canada

Summary:  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.

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