We use the analytic methods and the properties of Gauss sums to study one kind mean value problems involving the classical Dedekind sums,and give an interesting identity and asymptotic formula for it.
For any real constants λ1, λ2 C (0, 1], let n ≥ max{[1/λ1 ], [1/λ2]}, vn ≥ 2 be integers. Suppose integers a C [1, λ1n] and b E [1, λ2n] satisfy the congruence b ≡ am (rood n). The main purpose of this pap...For any real constants λ1, λ2 C (0, 1], let n ≥ max{[1/λ1 ], [1/λ2]}, vn ≥ 2 be integers. Suppose integers a C [1, λ1n] and b E [1, λ2n] satisfy the congruence b ≡ am (rood n). The main purpose of this paper is to study the mean value of (a - b)2k for any fixed positive integer k and obtain some sharp asymptotic formulae.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11001218 and 11071194)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20106101120001)
文摘We use the analytic methods and the properties of Gauss sums to study one kind mean value problems involving the classical Dedekind sums,and give an interesting identity and asymptotic formula for it.
基金supported by National Natural Science Foundation of China (Grant No. 11001218)the Research Fund for the Doctoral Program of Higher Education of China (Grant No.20106101120001)
文摘For any real constants λ1, λ2 C (0, 1], let n ≥ max{[1/λ1 ], [1/λ2]}, vn ≥ 2 be integers. Suppose integers a C [1, λ1n] and b E [1, λ2n] satisfy the congruence b ≡ am (rood n). The main purpose of this paper is to study the mean value of (a - b)2k for any fixed positive integer k and obtain some sharp asymptotic formulae.