This article reveals bounds and formulas for logarithmic derivatives in number fields, suggesting deeper arithmetic insights.
The higher Euler-Kronecker constants of a number field K are the coefficients appearing in the Laurent series expansion of the logarithmic derivative of the Dedekind zeta function about s = 1. These coefficients are mysterious and seem to contain a lot of arithmetic information. In this article, we study these coefficients. We prove arithmetic formulas and bounds satisfied by them, generalizing certain results of Ihara.
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Samprit Ghosh (2025) studied this question.
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