Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Sumaia Saad Eddin

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Abstract

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 $\gamma_{n}(K)$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 10 (2018), 93-96.

Dates
First available in Project Euclid: 26 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1543201231

Digital Object Identifier
doi:10.3792/pjaa.94.93

Mathematical Reviews number (MathSciNet)
MR3879319

Zentralblatt MATH identifier
07067285

Subjects
Primary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Keywords
Stieltjes constants Riemann zeta function Dedekind zeta function

Citation

Saad Eddin, Sumaia. The signs of the Stieltjes constants associated with the Dedekind zeta function. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 10, 93--96. doi:10.3792/pjaa.94.93. https://projecteuclid.org/euclid.pja/1543201231


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