The higher Euler-Kronecker constants of a number field K are the coefficients appearing in the Laurent series expansion of the logarithmic derivative of the Dedekind zeta function about s = 1. These coefficients are mysterious and seem to contain a lot of arithmetic information. In this article, we study these coefficients. We prove arithmetic formulas and bounds satisfied by them, generalizing certain results of Ihara.
Samprit Ghosh (Thu,) studied this question.