On certain character sums over $\mathbb {F}_q[T]$
HTML articles powered by AMS MathViewer
- by Chih-Nung Hsu PDF
- Proc. Amer. Math. Soc. 126 (1998), 647-652 Request permission
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
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- E. Artin, ‘Quadratische Körper im Gebiete der höheren Kongruenzen I, II’, Math. Zeitschrift 19 (1924), pp. 153-246.
- 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
- Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
- 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
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
- Received by editor(s): August 20, 1996
- Communicated by: Dennis A. Hejhal
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 647-652
- MSC (1991): Primary 11A07; Secondary 11L40, 11N05
- DOI: https://doi.org/10.1090/S0002-9939-98-04582-1
- MathSciNet review: 1469411