Special values of spectral zeta functions of graphs and Dirichlet LL-functions

In this paper, we establish relations between special values of Dirichlet $L$-functions and that of spectral zeta functions or $L$-functions of cycle graphs. In fact, they determine each other in a natural way. These two kinds of special values were bridged together by a combinatorial derivative formula obtained from studying spectral zeta functions of the first order self-adjoint differential operators on the unit circle

On a certain non-split cubic surface

In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface $$x_0(x_1^2 + x_2^2)=x_3^3$$ with a power-saving error term, which verifies the Manin-Peyre conjectures for this surface.Comment: v2. 18 pages, one author adde

USING SOCIAL NETWORK ANALYSIS AS A STRATEGY FOR E-COMMERCE RECOMMENDATION

Recommender agents are being widely used by E-commerce business to help customers make decisions from a large amount of choices. To improve the performance of recommendation agents, three main approaches (content-based approaches, collaborative approaches and hybrid approaches) have been proposed to address recommendation problem whose basic idea is to discover similarity of items and users and predicate users’ preference toward a set of items. This provides potential for using social network analysis to make recommendations since social network analysis can be used to investigate the relationships of customers. In this research, we illustrate the concepts of social network analysis and how it can be employed to make better recommendations in E-commerce context. Application and research opportunities are presented