Journal of the Ramanujan Mathematical Society

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The Chebotarev Density Theorem and the Pair Correlation Conjecture


Affiliations
1 Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
2 Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
     

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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 ischolar_main conjecture and the Lang-Trotter conjectures and obtain shaper error terms.
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  • The Chebotarev Density Theorem and the Pair Correlation Conjecture

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Authors

M. Ram Murty
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
V. Kumar Murty
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
Peng-Jie Wong
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada

Abstract


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 ischolar_main conjecture and the Lang-Trotter conjectures and obtain shaper error terms.

References