The distribution of Euler-Kronecker constants of quadratic fields

[摘要] We investigate the distribution of large positive (and negative) values of the Euler Kronecker constant gamma(Q(root D)) of the quadratic field Q(root D) as D varies over fundamental discriminants vertical bar D vertical bar <= x. We show that the distribution function of these values is very well approximated by that of an adequate probabilistic random model in a large uniform range. The main tools are an asymptotic formula for the Laplace transform of gamma(Q(root D)) together with a careful saddle point analysis. (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Euler-Kronecker constants;Dedekind zeta function;Dirichlet L-functions;The saddle-point method