On polynomial reciprocity law.
type: Item
instance of: scholarly article
title: On polynomial reciprocity law.
zbMATH Open document ID: 1115.11069
DOI: 10.1016/S0022-314X(03)00020-9
author: Chih-Nung Hsu
published in: Journal of Number Theory
publication date: 2003-07-30T00:00:00Z
review text: The quadratic reciprocity law was generalized to polynomials by Carlitz. Here we have another proof deduced from an appropriate generalization to polynomials of Jacobi symbols, namely the author considers essentially \[ \text{Jacobi}(a,m) = \text{Resultant}(n,a). \] Where \(n\) is the unique monic polynomial scalar multiple of \(m.\) A polynomial version of the biquadratic law of reciprocity is also obtained. Moreover, by using analytic methods, the author is able to generalize appropriately also the value of quadratic Gauss sums.
Mathematics Subject Classification ID: 11T55
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 11A15
zbMATH DE Number: 1957099
zbMATH Keywords: polynomial rings
zbMATH Keywords: finite fields
zbMATH Keywords: Jacobi symbol
zbMATH Keywords: reciprocity laws
reviewed by: Luis Gallardo
MaRDI profile type: Publication
cites work: Ein rationales biquadratisches Reziprozitätsgesetz.
cites work: Average values of L-series in function fields.
cites work: Q3999066
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cites work: On quadratic reciprocity over function fields
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full work available at URL: s0022-314x(03)00020-9
OpenAlex ID: W2082430530
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description: scientific article; zbMATH DE number 1957099