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(11161006)Guan-gxi Natural Science Foundation(2010GXNSFB013048,2011GXNSFA018139)Scientific Research Foundation of Guangxi Educational Committee(201012MS140)
基金supported by the National Natural Science Foundation of China (10771095)the Guangxi Science Foundation(0832107,0991102)the Scientific Research Foundation of Guangxi Educational Committee (200707LX233)
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.
