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On a converse to the Tschebotarev density theorem
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 ? 8. 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.
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Publication status
- Published
Journal
Journal of the Australian Mathematical Society (Series A)ISSN
1446-7887Publisher
Cambridge University PressExternal DOI
Issue
3Volume
44Page range
287-293Department affiliated with
- Business and Management Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-09-26Usage metrics
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