Reciprocity and jacobi sums

Joseph B. Muskat

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)275-280
Number of pages6
JournalPacific Journal of Mathematics
Issue number2
StatePublished - Feb 1967


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