Ray class invariants over imaginary quadratic fields

Let $K$ be an imaginary quadratic field of discriminant less than or equal to -7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater than 1. We prove that singular values of certain Siegel functions generate $K_{(N)}$ over $K$ by extending the idea of our previous work. These generators are not only the simplest ones conjectured by Schertz, but also quite useful in the matter of computation of class polynomials. We indeed give an algorithm to find all conjugates of such generators by virtue of Gee and Stevenhagen

An IT Tool for Increasing Productivity of Knowledge Workers and Their Organizations

Productivity in making and moving things hasincreased at an annual rate of 3 to 4 percent compounded for the last 125 years -or a 45-fold expansion in overall productivity in the devel-oped countries. However, there has not been such a big improvement in knowledge worker\u27s productivity. A knowledge worker is a profes-sional who applies ideas, concepts, and informa-tion to work rather than manual skills or brawn [4]. In some developed countries, knowledge workers represent approximately 80% of all employees and perform key roles in economic activities in an enterprise. Therefore, the produc-tivity of the newly dominant groups in the work force, i.e., knowledge workers, will be the big-gest and toughest challenge facing managers in the developed countries for decades to come. Also, some analysts forecast that the stagnation of productivity of knowledge workers will emerge as one of the obstacles to maintain an appropriate level of growth for the twenty first centur

Arithmetic properties of orders in imaginary quadratic fields

Let $K$ be an imaginary quadratic field. For an order $\mathcal{O}$ in $K$ and a positive integer $N$, let $K_{\mathcal{O},\,N}$ be the ray class field of $\mathcal{O}$ modulo $N\mathcal{O}$. We deal with various subjects related to $K_{\mathcal{O},\,N}$, mainly about Galois representations attached to elliptic curves with complex multiplication, form class groups and $L$-functions for orders