DIVISIBILITY OF EXPONENTIAL SUMS AND SOLVABILITY OF CERTAIN EQUATIONS OVER FINITE FIELDS

Carlitz [Solvability of certain equations in a finite field, Quart. J. Math. (Oxford) 7 (1956), 3–4] determined conditions under which infinite families of polynomials have solutions in a finite field. In this paper we extend some of Carlitz's results by computing the exact p-divisibility of ce...

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Bibliographic Details
Published in:Quarterly journal of mathematics 2009-06, Vol.60 (2), p.169-181
Main Authors: Castro, Francis N., Rubio, Ivelisse, Vega, José M.
Format: Article
Language:English
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Summary:Carlitz [Solvability of certain equations in a finite field, Quart. J. Math. (Oxford) 7 (1956), 3–4] determined conditions under which infinite families of polynomials have solutions in a finite field. In this paper we extend some of Carlitz's results by computing the exact p-divisibility of certain exponential sums. As a by-product we obtain an upper bound for the Waring number for polynomials over extensions of finite fields.
ISSN:0033-5606
1464-3847
DOI:10.1093/qmath/han013