The distribution of Euler-Kronecker constants of quadratic fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Lamzouri, Youness

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

DOI  :  10.1016/j.jmaa.2015.06.065

来源: Elsevier

【 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.

【 授权许可】

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