Vol. 20, No. 2, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Reciprocity and Jacobi sums

Joseph Baruch Muskat

Vol. 20 (1967), No. 2, 275–280
Abstract

Recently N. C. Ankeny derived a law of r-th power reciprocity, where !r is an odd prime: q is an r-th power residue, modulo p 1( mod r), if and only if the r-th power of the Gaussian sum (or Lagrange resolvent) τ(χ), which depends upon p and r, is an r-th power in GF(qf), where q belongs to the exponent f( mod r). τ(χ)r can be written as the product of algebraic integers known as Jacobi sums. Conditions in which the reciprocity criterion can be expressed in terms of a single Jacobi sum are presented in this paper.

Mathematical Subject Classification
Primary: 10.06
Milestones
Received: 19 January 1966
Published: 1 February 1967
Authors
Joseph Baruch Muskat