Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $P$.

References [Enhancements On Off] (What's this?)

  • 1. N. C. Ankeny, The least quadratic non residue, Ann. of Math. (2) 55 (1952), 65–72. MR 0045159 (13,538c)
  • 2. E. Artin, `Quadratische Körper im Gebiete der höheren Kongruenzen I, II', Math. Zeitschrift 19 (1924), pp. 153-246.
  • 3. Gove W. Effinger and David R. Hayes, Additive number theory of polynomials over a finite field, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1143282 (92k:11103)
  • 4. G. H. Hardy and E. M. Wright, `An Introduction to the Theory of Numbers', Oxford, Clarendon Press (1945). MR 16:673c (3rd ed.)
  • 5. Serguei A. Stepanov, Arithmetic of algebraic curves, Monographs in Contemporary Mathematics, Consultants Bureau, New York, 1994. Translated from the Russian by Irene Aleksanova. MR 1321599 (95j:11055)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11A07, 11L40, 11N05

Retrieve articles in all journals with MSC (1991): 11A07, 11L40, 11N05

Additional Information

Chih-Nung Hsu
Affiliation: Department of Mathematics, National Taiwan Normal University, 88 Sec. 4 Ting-Chou Road, Taipei, Taiwan

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia