On polynomial reciprocity law

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The well-known law of quadratic reciprocity has over 150 proofs in print. We establish a relation between polynomial Jacobi symbols and resultants of polynomials over finite fields. Using this relation, we prove the polynomial reciprocity law and obtain a polynomial analogue of classical Burde's quartic reciprocity law. Under the use of our polynomial Poisson summation formula and the evaluation of polynomial exponential map, we get a reciprocity for the generalized polynomial quadratic Gauss sums.

Original languageEnglish
Pages (from-to)13-31
Number of pages19
JournalJournal of Number Theory
Volume101
Issue number1
DOIs
Publication statusPublished - 2003 Jul 1

Keywords

  • Finite fields
  • Polynomial rings
  • Reciprocity law

ASJC Scopus subject areas

  • Algebra and Number Theory

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