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자연과학대학
수학전공
Journal papers
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Regulators of an infinite family of the simplest quartic function fields
Title
Regulators of an infinite family of the simplest quartic function fields
Authors
Lee J.
;
Lee Y.
Ewha Authors
이윤진
;
이정연
SCOPUS Author ID
이윤진
; 이정연
Issue Date
2017
Journal Title
Canadian Journal of Mathematics
ISSN
0008-414X
Citation
Canadian Journal of Mathematics vol. 69, no. 3, pp. 579 - 594
Keywords
Class number
;
Function field
;
Quartic extension
;
Regulator
Publisher
Canadian Mathematical Society
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
We explicitly find regulators of an infinite family {Lm} of the simplest quartic function fields with a parameter m in a polynomial ring Fq [t], where Fq 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 {Lm } and some result on the divisibility of the divisor class numbers of cyclotomic function fields that contain {Lm} as their subfields. Furthermore, we find an explicit criterion for the characterization of splitting types of all the primes of the rational function field Fq(t) in {Lm}. © Canadian Mathematical Society 2016.
DOI
10.4153/CJM-2016-038-2
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