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arXiv · 1707.01622

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

Sumaia Saad Eddin
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Abstract

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

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Sumaia Saad Eddin. 2017-12-02. The signs of the Stieltjes constants associated with the Dedekind zeta function. https://arxiv.org/abs/1707.01622

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