ON THE γ-TH HYPER-KLOOSTERMAN SUMS AND A PROBLEM OF D. H. LEHMER

Title & Authors
ON THE γ-TH HYPER-KLOOSTERMAN SUMS AND A PROBLEM OF D. H. LEHMER
Tianping, Zhang; Xifeng, Xue;

Abstract
For any integer k $\small{\geq}$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($\small{a_1,a_2,...,a_{k+1}}$) such that $\small{1{\leq}a_i{\leq}q}$, ($\small{a_i,q}$) = 1, $\small{a_1a_2...a_{k+1}{\equiv}}$ c (mod q) and 2 $\small{\nmid}$ ($\small{a_1+a_2+...+a_{k+1}}$), and E(c, k+1; q) = P(c, k+1;q) - $\small{\frac{{\phi}^k(q)}{2}}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.⠍瘀܀㔷㠮㐵㬗L楦攠獣楥湣敳…⁢楯汯杹
Keywords
r-th hyper-Kloosterman sums;hybrid mean value;
Language
English
Cited by
1.
Modular hyperbolas, Japanese Journal of Mathematics, 2012, 7, 2, 235
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