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RISS 인기검색어
- 검색키워드
- 저자 : Xue Xifeng (검색결과 2 건)
- 무료
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- 유료
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ON THE γ-TH HYPER-KLOOSTERMAN SUMS AND A PROBLEM OF D. H. LEHMER
Tianping, Zhang,Xifeng, Xue Korean Mathematical Society 2009 대한수학회지 Vol.46 No.4
For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. 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.
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On the r-th hyper-Kloosterman sums and a problem of D. H. Lehmer
Zhang Tianping,Xue Xifeng 대한수학회 2009 대한수학회지 Vol.46 No.4
For any integer k≥2, let P(c,k+1;q) be the number of all k+1-tuples with positive integer coordinates (a_1, a_2,…,a_{k+1}) such that 1≤a_i≤q, (a_i, q)=1,a_1 a_2…a_{k+1}≡ c(mod q) and 2│(a_1+a_2+…+a_{k+1}), and E(c,k+1;q)=P(c,k+1;q)-Φi^{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. For any integer k≥2, let P(c,k+1;q) be the number of all k+1-tuples with positive integer coordinates (a_1, a_2,…,a_{k+1}) such that 1≤a_i≤q, (a_i, q)=1,a_1 a_2…a_{k+1}≡ c(mod q) and 2│(a_1+a_2+…+a_{k+1}), and E(c,k+1;q)=P(c,k+1;q)-Φi^{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.
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