Vol. 20, No. 2, 1967

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Reciprocity and Jacobi sums

Joseph Baruch Muskat

Vol. 20 (1967), No. 2, 275–280

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
Received: 19 January 1966
Published: 1 February 1967
Joseph Baruch Muskat