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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.
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참고문헌 (24)
참고문헌 신청
A. J. Lazarus / 1991 / On the class number and unit index of simplest quartic fields / Nagoya Math. J 121 : 1 ~ 13
A. Stein / 1999 / Some methods for evaluating the regulator of a real qua-dratic function field / Experiment. Math 8 (2) : 119 ~ 133
D. H. Lehmer / 1993 / The Lehmer project / Math. Comp 61 (203) : 313 ~ 317
D. Shanks / 1974 / The simplest cubic fields / Math. Comp 28 : 1137 ~ 1152
E. Lehmer / 1988 / Connection between Gaussian periods and cyclic units / Math. Comp 50 (182) : 535 ~ 541
A. Stein / 1999 / Some methods for evaluating the regulator of a real qua-dratic function field / Experiment. Math 8 (2) : 119 ~ 133
D. H. Lehmer / 1993 / The Lehmer project / Math. Comp 61 (203) : 313 ~ 317
D. Shanks / 1974 / The simplest cubic fields / Math. Comp 28 : 1137 ~ 1152
E. Lehmer / 1988 / Connection between Gaussian periods and cyclic units / Math. Comp 50 (182) : 535 ~ 541
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