On a converse to the Tschebotarev density theorem

van der Ploeg, Carol (1988) On a converse to the Tschebotarev density theorem. Journal of the Australian Mathematical Society (Series A), 44 (3). pp. 287-293. ISSN 1446-7887

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Abstract

Using an elementary counting procedure on biquadratic polynomials over Zp it is shown that the probability distribution of odd, unramified rational primes according to decomposition type in a fixed dihedral numberfield is identical to the probility of separable quartic polynomials (mod p) whose roots generate numberfields with normal closure having Galois group isomorphic to D4, as p → ∞. This verifies a conjecture about a converse to the Tschebotarev density theorem. Further evidence in support of this conjecture is provided in quadratic and coubic numberfields.

Item Type: Article
Schools and Departments: School of Business, Management and Economics > Business and Management
Subjects: Q Science > QA Mathematics > QA0150 Algebra. Including machine theory, game theory
Depositing User: Carol Alexander
Date Deposited: 26 Sep 2012 08:22
Last Modified: 27 Sep 2012 07:47
URI: http://sro.sussex.ac.uk/id/eprint/40630
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