<abstract xmlns="http://www.w3.org/1999/xhtml">

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

In a family of Sn-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 dK+ O(log log log dK) and loglog dK + O(log log log dK), resp., where dK is the absolute value of the discriminant of a number field K.

Extreme Values of Euler-Kronecker Constants

Uniform distribution theory

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{"article-title":"Extreme Values of Euler-Kronecker Constants"}

In a family of Sn-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...

Extreme Values of Euler-Kronecker Constants

Published Online: Oct 30, 2021

Page range: 41 - 52

Received: Jan 13, 2021

Accepted: Apr 06, 2021

DOI: https://doi.org/10.2478/udt-2021-0002

Keywords
Euler-Kronecker constants, Dedekind zeta functions, Logarithmic derivatives of -functions

© 2021 Henry H. Kim et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Extreme Values of Euler-Kronecker Constants

Published Online: Oct 30, 2021

Page range: 41 - 52

Received: Jan 13, 2021

Accepted: Apr 06, 2021

DOI: https://doi.org/10.2478/udt-2021-0002

KeywordsEuler-Kronecker constants, Dedekind zeta functions, Logarithmic derivatives of -functions

© 2021 Henry H. Kim et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Euler-Kronecker constants, Dedekind zeta functions, Logarithmic derivatives of -functions