On Euler-Kronecker constants and the generalized Brauer-Siegel\n conjecture

2019/08/08 by Anup B. Dixit, Dixit, Anup B.
Arts and Humanities · Mathematics · #11R18 #11R29 #11R42 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1908.03044

openalex publication_date 2019/08/08 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

As a natural generalization of the Euler-Mascheroni constant \γ, Y.\nIhara introduced the Euler-Kronecker constant \γ_K attached to any number\nfield K. In this paper, we prove that a certain bound on \γ_K in a\ntower of number fields \K implies the generalized Brauer-Siegel\nconjecture for \K as formulated by Tsfasman and Vl vadu ct.\nMoreover, we use known bounds on \γ_K for cyclotomic fields to obtain a\nfiner estimate for the number of zeros of the Dedekind zeta-function\n\ζ_K(s) in the critical strip.\n

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• Relative class numbers and Euler-Kronecker constants of maximal real cyclotomic subfields
• Asymptotic properties of Dedekind zeta functions in families of number fields
• Higher Euler-Kronecker Constants of Number fields
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