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Note on the mean value of higher-Kloosterman sums
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It is difficult to study the mean value properties of the higher-Kloosterman sums S(m, n, q; k) for any positive integer k. In this paper, the fourth power mean of this exponential sums is studied by combining congruence theorey with the analytic method, and an interesting asymptotic formula for it is obtained. The new result is an important generalization and improvement of the previous.
higher-Kloosterman sumstrigonometric identityasmptotic formula
YAO Wei-li、CAO Tie-ming、WANG Qin-qin
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Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China
School of Science, Xi'an Shiyou University, Xi'an 710065, P. R. China
Special Foundation for Excellent Young Teacher to Scientific ResearchInnovation Foundation of Shanghai University