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The signs of the Stieltjes constants associated with the Dedekind zeta function. (English) Zbl 1453.11148

Summary: 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 \(\gamma_{n}(\mathbb{Q})\). We also study the signs of \(\gamma_{n}(K)\).

MSC:

11R42 Zeta functions and \(L\)-functions of number fields
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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