On certain character sums over ℙq,[T]

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Abstract

Let ℙq be the finite field with q elements and let A denote the . ring of polynomials in one variable with coefficients in ℙq. Let P be a monic polynomial irreducible in A. We obtain a bound for the least degree of a monic polynomial irreducible in A (q odd) which is a quadratic non-residue modulo P. We also find a bound for the least degree of a monic polynomial irreducible . in A which is a primitive root modulo P.

Original languageEnglish
Pages (from-to)647-652
Number of pages6
JournalProceedings of the American Mathematical Society
Volume126
Issue number3
Publication statusPublished - 1998 Dec 1

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Keywords

  • Primitive roots
  • Quadratic non-residues
  • Riemann Hypothesis

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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