A note on the \(d\)th power residue symbol of \(\mathbb F_q[t]\)
type: Item
instance of: scholarly article
title: A note on the \(d\)th power residue symbol of \(\mathbb F_q[t]\)
zbMATH Open document ID: 1221.11006
author: Su Hu
published in: Journal of Number Theory
publication date: 2008-11-18T00:00:00Z
review text: \textit{S. Wright} [J. Number Theory 128, No. 4, 918--925 (2008; Zbl 1167.11006)] found a necessary and sufficient criterion for any nonempty set \(S\) to have the following property: for any fixed nonnegative integer \(q\), there exist infinitely many primes \(p\) such that \(S\) contains exactly \(q\) quadratic residues modulo \(p\). His criterion is expressed by means of a purely combinatorial condition on the prime factors of the elements of \(S\) of odd multiplicity. In this paper the author generalizes Wright's result to \(d\)th power residue symbols for polynomial rings over finite fields.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11A15
zbMATH DE Number: 5368236
zbMATH Keywords: \(d\)th power residue symbol
zbMATH Keywords: polynomial ring
zbMATH Keywords: residue representative
zbMATH Keywords: residue partition
MaRDI profile type: Publication
full work available at URL: j.jnt.2007.10.009
OpenAlex ID: W1990684395
cites work: Q2776773
cites work: Patterns of quadratic residues and nonresidues for infinitely many primes
cites work: Quadratic residues and the combinatorics of sign multiplication
DOI: 10.1016/J.JNT.2007.10.009
description: scientific article; zbMATH DE number 5368236