Let = be a fundamental unit in a real quadratic field and let S be the set of rational primes p for which = has maximal order modulo p. Under the assumption of the generalized Riemann hypothesis, we show that S has a density $(S)=c } A in the set of all rational primes, where A is Artin's constant a
An analogue of Artin's conjecture for Abelian extensions
β Scribed by M.Ram Murty
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 262 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0022-314X
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It is a pleasure to thank the referec for his valuable suggestions which resulted in an improvement of the manuscript. The first author also thanks Professor E. L. Green for valuable discussions concerning the package GRB, on May 1994 at SFB 343, University Bielefeld; and Professor C. M. Ringel for
when A is a torsion-free abelian group of rank one. As a consequence he was able to show that a finite rank torsion-free group M satisfies M ( nat M\*\* if and only if M F A I and pM s M precisely when pA s A, where Ε½ . M\*sHom y, A . Using this Warfield obtained a characterization of Z Ε½ . w x the
## Abstract We will show the Hodge conjecture and the Tate conjecture are true for the Hilbert schemes of points on an abelian surface or on a Kummer surface. (Β© 2006 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)