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On a Converse to the Tscgebotarev density theorem

Published online by Cambridge University Press:  09 April 2009

C. E. Van Der Ploeg
C. E. Van Der Ploeg
Affiliation:
Mathematics DivisonUniversity of SussexFalmer, Brighton United Kingdom
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Abstract

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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.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 3 , June 1988 , pp. 287 - 293
Copyright
Copyright © Australian Mathematical Society 1988

References

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