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Degree matrices and divisibility of exponential sums over finite fields. (English) Zbl 1217.11118

Summary: By using the degree matrix, we provide an elementary and algorithmic approach to estimating the divisibility of exponential sums over prime fields, which improves the Adolphson-Sperber theorem obtained by using the Newton polyhedron. Our result also improves the Ax-Katz theorem on estimating the number of rational points on hypersurfaces over prime fields.

MSC:

11T23 Exponential sums
11H06 Lattices and convex bodies (number-theoretic aspects)
11D79 Congruences in many variables
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