A counterexample to an analogue of Artin’s conjecture
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- by P. J. Weinberger PDF
- Proc. Amer. Math. Soc. 35 (1972), 49-52 Request permission
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
- Larry Joel Goldstein, Analogues of Artin’s conjecture, Bull. Amer. Math. Soc. 74 (1968), 517–519. MR 223328, DOI 10.1090/S0002-9904-1968-11987-1
- Larry Joel Goldstein, Analogues of Artin’s conjecture, Trans. Amer. Math. Soc. 149 (1970), 431–442. MR 279066, DOI 10.1090/S0002-9947-1970-0279066-3
- Helmut Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952 (German). MR 0049239
- Karl Prachar, Primzahlverteilung, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 91, Springer-Verlag, Berlin-New York, 1978 (German). Reprint of the 1957 original. MR 516660
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 49-52
- MSC: Primary 12A65
- DOI: https://doi.org/10.1090/S0002-9939-1972-0299582-5
- MathSciNet review: 0299582