56 citations · 90 across the 26 of their papers we have counts for
27 papers
On some sums involving the counting function of non-isomorphic abelian groups
Haihong Fan, Wenguang Zhai
Let denote the number of non-isomorphic abelian groups with elements. In 1991 Ivić proved an asymptotic formula of the sum In this paper, we…
Continued fraction formulae involving ratios of three gamma functions
Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai
Via the MC-algorithm, in this paper we produce seven continued fraction formulae involving products and quotients of three gamma functions with three parameters, and another is an…
The average size of Ramanujan sums over quadratic number fields(II)
Wenguang Zhai
In this paper we study Ramanujan sums , where and are integral ideals in an arbitrary quadratic number field. We give some new results about…
The Average Size of Ramanujan Sums over Cubic Number Fields
Jing Ma, Huayan Sun, Wenguang Zhai
Let K be a cubic number field. In this paper, we study the Ramanujan sums c_{J}(I), where I and J are integral ideals in O_{K}. The asymptotic behaviour of sums of c_{J}(I) over bo…
Average of Hardy's function at Gram points
Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai
Let be Hardy's function and be the -th Gram points defined by . Titchmarsh proved that $\sum_{n \leq N} Z(…
Some mean value results related to Hardy's function
Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai
Let and be the Riemann zeta function and Hardy's function respectively. We show asymptotic formulas for and .…