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A counterexample to an analogue of Artin's conjecture

Author: P. J. Weinberger
Journal: Proc. Amer. Math. Soc. 35 (1972), 49-52
MSC: Primary 12A65
MathSciNet review: 0299582
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Abstract: I construct a counterexample to a conjecture of Larry Goldstein on the density of primes which split completely in none of a set of algebraic number fields. The fields used are all Abelian over the rationals.

References [Enhancements On Off] (What's this?)

  • [1] Larry Joel Goldstein, Analogues of Artin's conjecture, Bull. Amer. Math. Soc. 74 (1968), 517-519. MR 36 #6376. MR 0223328 (36:6376)
  • [2] -, Analogues of Artin's conjecture, Trans. Amer. Math. Soc. 149 (1970), 431-442. MR 0279066 (43:4792)
  • [3] Helmut Hasse, Über die Klassenzahl Abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952. MR 14, 141. MR 0049239 (14:141a)
  • [4] Karl Prachar, Primzahlverteilung, Springer-Verlag, Berlin and New York, 1952. MR 19, 393. MR 516660 (81k:10060)

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Article copyright: © Copyright 1972 American Mathematical Society

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