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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On certain character sums over $\protect\mathbb F_q[T]$


Author: Chih-Nung Hsu
Journal: Proc. Amer. Math. Soc. 126 (1998), 647-652
MSC (1991): Primary 11A07; Secondary 11L40, 11N05
MathSciNet review: 1469411
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Abstract: Let ${\mathbb F}_{\!q}$ be the finite field with $q$ elements and let $\mathbf{A}$ denote the ring of polynomials in one variable with coefficients in ${\mathbb F}_{\!q}$. Let $P$ be a monic polynomial irreducible in $\mathbf{A}$. We obtain a bound for the least degree of a monic polynomial irreducible in $\mathbf{A}$ ($q$ odd) which is a quadratic non-residue modulo $P$. We also find a bound for the least degree of a monic polynomial irreducible in $\mathbf{A}$ which is a primitive root modulo $P$.


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Additional Information

Chih-Nung Hsu
Affiliation: Department of Mathematics, National Taiwan Normal University, 88 Sec. 4 Ting-Chou Road, Taipei, Taiwan
Email: maco@math.ntnu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04582-1
PII: S 0002-9939(98)04582-1
Keywords: Riemann Hypothesis, quadratic non-residues, primitive roots
Received by editor(s): August 20, 1996
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1998 American Mathematical Society