Asymptotic behaviour of theeuler–kronecker constant

Abstract

This appendix to the beautiful paper [1] of Ihara puts it in the context of infinite global fields of our papers [2] and [3]. We study the behaviour of Euler–Kronecker constant γK when the discriminant (genus in the function field case) tends to infinity. Results of [2] easily give us good lower bounds on the ratio γK/ log (Formula Presented). In particular, for number fields, under the generalized Riemann hypothesis we prove lim inf (Formula Presented) Then we produce examples of class-field towers, showing that lim inf (Formula Presented).