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FUNDAMENTAL UNITS AND REGULATORS OF AN INFINITE FAMILY OF CYCLIC QUARTIC FUNCTION FIELDS

이윤진|이정연
대한수학회 (The Korean Mathematical Society)|2017.03|대한수학회지 (Journal of the KMS)|제54권 제2호|pp. 417-426

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참고문헌

키워드

regulatorfunction fieldquintic extension
주제분류수학

초록

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.

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.

참고문헌 (24)

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