Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonmonomial characters and Artin's conjecture


Author: Richard Foote
Journal: Trans. Amer. Math. Soc. 321 (1990), 261-272
MSC: Primary 11R42; Secondary 11R32
MathSciNet review: 987161
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ E/F$ is a Galois extension of number fields with solvable Galois group $ G$, the main result of this paper proves that if the Dedekind zeta-function of $ E$ has a zero of order less than $ {\mathcal{M}_G}$ at the complex point $ {s_0} \ne 1$, then all Artin $ L$-series for $ G$ are holomorphic at $ {s_0}$ -- here $ {\mathcal{M}_G}$ is the smallest degree of a nonmonomial character of any subgroup of $ G$. The proof relies only on certain properties of $ L$-functions which are axiomatized to give a purely character-theoretic statement of this result.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11R42, 11R32

Retrieve articles in all journals with MSC: 11R42, 11R32


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0987161-9
PII: S 0002-9947(1990)0987161-9
Article copyright: © Copyright 1990 American Mathematical Society