The signs of the Stieltjes constants associated with the Dedekind zeta function

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Sumaia Saad Eddin¹ 

[1] Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University

关键词: Stieltjes constants;    Riemann zeta function;    Dedekind zeta function.Quasi-log canonical pairs;    normalization;    Du Bois singularities.Quasi-symmetries;    rigidity;    determinantal point process (DPP);    de Branges space.;   

DOI  :  10.3792/pjaa.94.93

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

The Stieltjes constants $\gamma_{n}(K)$ of a number field $K$ are the coefficients of the Laurent expansion of the Dedekind zeta function $\zeta_{K}(s)$ at its pole $s=1$. In this paper, we establish a similar expression of $\gamma_{n}(K)$ as Stieltjes obtained in 1885 for $\gamma_{n}(\mathbf{Q})$. We also study the signs of $\gamma_{n}(K)$.

【 授权许可】

Unknown