Regulators of an Infinite Family of the Simplest Quartic Function Fields
- 주제(키워드) regulator , function field , quartic extension , class number
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 CANADIAN MATHEMATICAL SOC
- 발행년도 2017
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000144753
- 본문언어 영어
- Published As http://dx.doi.org/10.4153/CJM-2016-038-2
초록/요약
We explicitly find regulators of an infinite family {L-m} of the simplest quartic function fields with a parameter m in a polynomial ring F-q [t], where F-q is the finite field of order q with odd characteristic. In fact, this infinite family of the simplest quartic function fields are subfields of maximal real subfields of cyclotomic function fields having the same conductors. We obtain a lower bound on the class numbers of the family {L-m} and some result on the divisibility of the divisor class numbers of cyclotomic function fields that contain {L-m} as their subfields. Furthermore, we find an explicit criterion for the characterization of splitting types of all the primes of the rational function field F-q(t) in {L-m}.
more