Solvability of Systems of Two Polynomial Equations over Finite Fields
نویسنده
چکیده
In this paper we determine the solvability of families of systems of two polynomial equations over finite fields by computing the exact divisibility of the exponential sums associated to the systems. This generalizes a theorem of Carlitz to systems of two equations. Our result gives an upper bound for the Waring number of systems of diagonal equations. Also, as a by-product, we also obtain information about the p-divisibility of the number of solutions of the systems for cases for which the well known results of Chevalley-Warning and Katz do not give any information.
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تاریخ انتشار 2009