Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

A Generalization of the Aramata-Brauer Theorem

Sandra L. Rhoades
Proceedings of the American Mathematical Society
Vol. 119, No. 2 (Oct., 1993), pp. 357-364
DOI: 10.2307/2159915
Stable URL: http://www.jstor.org/stable/2159915
Page Count: 8
  • Read Online (Free)
  • Download ($30.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
A Generalization of the Aramata-Brauer Theorem
Preview not available

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 ζE(s)/ζF(s) is entire, where this is the quotient of the Dedekind ζ-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.

Page Thumbnails

  • Thumbnail: Page 
357
    357
  • Thumbnail: Page 
358
    358
  • Thumbnail: Page 
359
    359
  • Thumbnail: Page 
360
    360
  • Thumbnail: Page 
361
    361
  • Thumbnail: Page 
362
    362
  • Thumbnail: Page 
363
    363
  • Thumbnail: Page 
364
    364