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

Fingerprint

Reciprocity Law
Polynomial
Quadratic reciprocity
Poisson Summation Formula
Gauss Sums
Exponential Map
Polynomial Maps
Generalized Polynomials
Jacobi Polynomials
Reciprocity
Quartic
Galois field
Analogue
Evaluation

Keywords

  • Finite fields
  • Polynomial rings
  • Reciprocity law

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On polynomial reciprocity law. / Hsu, Chih Nung.

In: Journal of Number Theory, Vol. 101, No. 1, 01.07.2003, p. 13-31.

Research output: Contribution to journalArticle

Hsu, Chih Nung. / On polynomial reciprocity law. In: Journal of Number Theory. 2003 ; Vol. 101, No. 1. pp. 13-31.
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