Complex numbers similar to the generalized Bernoulli numbers and their applications

Abstract

Let χ be a primitive Dirichlet character modulo k ≥ 3. In this paper, we define complex numbers associated with χ, which we denote by Cr(χ) (r = 0, 1,…), and we discuss their properties and their relationships with the generalized Bernoulli numbers.

Method for calculating Dirichlet L-functions

“…The numerical studies are usually based on asymptotic formulas for ( , ). The authors [5,Theorem 3.9] gave asymptotic formulas for ( , ) which associated with a primitive character in terms of the generalized Bernoulli numbers ( ) ( = 0,1, … ), which are the coefficients in the power series expansion (see e.g., [6]):…”