Extreme Values of Euler-Kronecker Constants

Henry H. Kim

doi:10.2478/udt-2021-0002

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Extreme Values of Euler-Kronecker Constants

Uniform distribution theory

Volume 16 (2021): Issue 1 (June 2021)

By: Henry H. Kim

Open Access

|Oct 2021

Abstract

In a family of S_n-fields (n ≤ 5), we show that except for a density zero set, the lower and upper bounds of the Euler-Kronecker constants are −(n − 1) log log d_K+ O(log log log d_K) and loglog d_K + O(log log log d_K), resp., where d_K is the absolute value of the discriminant of a number field K.

References

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Articles in this issue

DOI: https://doi.org/10.2478/udt-2021-0002 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 41 - 52

Submitted on: Jan 13, 2021

Accepted on: Apr 6, 2021

Published on: Oct 30, 2021

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Euler-Kronecker constants,

Dedekind zeta functions,

Logarithmic derivatives of L-functions

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2021 Henry H. Kim, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 16 (2021): Issue 1 (June 2021)