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arXiv · 2411.17946

Higher Euler-Kronecker Constants of Number fields

Samprit Ghosh
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Abstract

The higher Euler-Kronecker constants of a number field $K$ are the coefficients 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 satisfied by them and prove bounds. We generalize certain results of Ihara.

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Samprit Ghosh. 2024-11-26. Higher Euler-Kronecker Constants of Number fields. https://doi.org/10.1142/s1793042126500521

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