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Turku Symposium on Number Theory in Memory of Kustaa Inkeri
May 31 - June 4, 1999
University of Turku
Turku, Finland

Organizers
Matti Jutila, Tauno Metsänkylä

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A note on the power residue symbol
by
Charles Helou
Pennsylvania State University, USA

It is well-known that Gauss gave six proofs of the quadratic reciprocity law with the aim of generalizing some of them to higher reciprocity laws. Many more proofs were given throughout the years by a number of authors. A relatively recent one by R. Swan in 1990 presents an expression for the quadratic residue symbol in terms of the norms of some elements in cyclotomic fields. We explore the extension of his method to higher power residue symbols.

Date received: March 11, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacf-10.