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arXiv · 1410.1603

The distribution of Euler-Kronecker constants of quadratic fields

Youness Lamzouri
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Abstract

We investigate the distribution of large positive (and negative) values of the Euler-Kronecker constant $γ_{\mathbb{Q}(\sqrt D)}$ of the quadratic field $\mathbb{Q}(\sqrt{D})$ as $D$ varies over fundamental discriminants $|D|\leq x$. 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 $γ_{\mathbb{Q}(\sqrt D)}$ together with a careful saddle point analysis.

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Youness Lamzouri. 2014-10-07. The distribution of Euler-Kronecker constants of quadratic fields. https://arxiv.org/abs/1410.1603

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