Higher Euler–Kronecker constants of number fields

The higher Euler–Kronecker constants of a number field [Formula: see text] are the coefficients appearing in the Laurent series expansion of the logarithmic derivative of the Dedekind zeta function about [Formula: see text]. These coefficients are mysterious and seem to contain a lot of arithmetic information. In this paper, we study these coefficients. We prove arithmetic formulas and bounds satisfied by them, generalizing certain results of Ihara.