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 Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

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)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
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