TY - JOUR

T1 - Reciprocity and jacobi sums

AU - Muskat, Joseph B.

PY - 1967/2

Y1 - 1967/2

N2 - Recently N. C. Ankeny derived a law of rth power reciprocity, where r is an odd prime: q is an rth power residue, modulo p = 1 (mod r), if and only if the rth power of the Gaussian sum (or Lagrange resolvent) τ(χ), which depends upon p and r, is an rth 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.

AB - Recently N. C. Ankeny derived a law of rth power reciprocity, where r is an odd prime: q is an rth power residue, modulo p = 1 (mod r), if and only if the rth power of the Gaussian sum (or Lagrange resolvent) τ(χ), which depends upon p and r, is an rth 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.

UR - http://www.scopus.com/inward/record.url?scp=84972535497&partnerID=8YFLogxK

U2 - 10.2140/pjm.1967.20.275

DO - 10.2140/pjm.1967.20.275

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AN - SCOPUS:84972535497

SN - 0030-8730

VL - 20

SP - 275

EP - 280

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -