A generalization of the Aramata-Brauer theorem
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- by Sandra L. Rhoades PDF
- Proc. Amer. Math. Soc. 119 (1993), 357-364 Request permission
Abstract:
The Aramata-Brauer Theorem says that the regular character minus the principal character of a finite group can be written as a positive rational linear combination of induced linear characters. In the language of Artin $L$-series this says that ${\zeta _E}(s)/{\zeta _F}(s)$ is entire, where this is the quotient of the Dedekind $\zeta$-functions of a Galois extension $E/F$ of number fields. Given any subset of characters of a finite group, we will give a necessary and sufficient condition for when a character is a positive rational linear combination of characters from this specified subset. This result implies that the regular character plus or minus any irreducible character can be written as a positive rational linear combination of induced linear characters. This both generalizes and gives a new proof of the Aramata-Brauer Theorem.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 357-364
- MSC: Primary 20C15; Secondary 11M41, 11R42
- DOI: https://doi.org/10.1090/S0002-9939-1993-1166360-8
- MathSciNet review: 1166360