A Sum Analogous to the Dedekind Sum and its Mean Value Formula

On a Sum Analogous to Dedekind Sum and Its Mean Square Value Formula

A New Sum Analogous to Gauss Sums and Its Fourth Power Mean

The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.

Mean Values of Generalized gcd-sum and lcm-sum Functions

We consider a generalization of the gcd-sum function, and obtain its average order with a quasi-optimal error term. We also study the reciprocals of the gcd-sum and lcm-sum functions.

A hybrid mean value involving a new Gauss sums and Dedekind sums

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...