Fundamental units and regulators of an infinite family of cyclic quartic function fields

Jungyun Lee; Yoonjin Lee

doi:10.4134/JKMS.j160002

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2017; 54(2): 417-426

Online first article November 17, 2016 Printed March 1, 2017

https://doi.org/10.4134/JKMS.j160002

Fundamental units and regulators of an infinite family of cyclic quartic function fields

Jungyun Lee and Yoonjin Lee

Ewha Womans University, Ewha Womans University

Abstract

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Abstract

We explicitly determine fundamental units and regulators of an infinite family of cyclic quartic function fields $L_h$ of unit rank 3 with a parameter $h$ in a polynomial ring $\F_q [t]$, where $\F_q$ is the finite field of order $q$ with characteristic not equal to $2$. This result resolves the second part of Lehmer's project for the function field case.

Keywords: regulator, function field, quintic extension

MSC numbers: 11R29, 11R58