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An explicit bound for
the least prime ideal in the Chebotarev density theorem
Jesse Thorner and Asif Zaman |
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Vol. 11 (2017), No. 5, 1135–1197
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Abstract |
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We prove an explicit version of Weiss’ bound on the least norm of a prime ideal in the Chebotarev density theorem, which is a significant improvement on the work of Lagarias, Montgomery, and Odlyzko. As an application, we prove the first explicit, nontrivial, and unconditional upper bound for the least prime represented by a positive-definite primitive binary quadratic form. We also consider applications to elliptic curves and congruences for the Fourier coefficients of holomorphic cuspidal modular forms. |
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Keywords
Chebotarev density theorem, least prime ideal, Linnik's
theorem, binary quadratic forms, elliptic curves, modular
forms, log-free zero density estimate
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Mathematical Subject Classification 2010
Primary: 11R44
Secondary: 11M41, 14H52
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Milestones
Received: 12 May 2016
Revised: 25 October 2016
Accepted: 10 March 2017
Published: 12 July 2017
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Authors |
| Jesse Thorner | |
| Department of Mathematics Stanford University Building 380 Sloan Mathematical Center Stanford, CA 94305 United States |
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| Asif Zaman | |
| Department of Mathematics University of Toronto Room 6290 40 St. George St. Toronto, ON M5S 2E4 Canada |
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