Degree matrices and divisibility of exponential sums over finite fields |
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| Authors: | Jianming Chen Wei Cao |
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| Institution: | 1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, People’s Republic ofChina
2. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China
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| Abstract: | 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. |
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