Higher Euler-Kronecker Constants of Number fields

2024/11/26 by Ghosh, Samprit · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2411.17946

openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Moments of Higher Logarithmic Derivatives and Exceptional Zeros in Cyclotomic Fields

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