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

Abstract

We explicitly determine fundamental units and regulators of an infinite family of cyclic quartic function fields Lh of unit rank 3 with a parameter h in a polynomial ring ��q[t], where ��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. © 2017 Korean Mathematical Society.