Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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FUNDAMENTAL UNITS AND REGULATORS OF AN INFINITE FAMILY OF CYCLIC QUARTIC FUNCTION FIELDS

  • Lee, Jungyun (Institute of Mathematical Sciences Ewha Womans University) ;
  • Lee, Yoonjin (Department of Mathematics Ewha Womans University)
  • Received : 2016.01.04
  • Published : 2017.03.01
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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 $\mathbb{F}_q[t]$, where $\mathbb{F}_q$ 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

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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