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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
이윤진이정연
SCOPUS Author ID
이윤진scopus; 이정연scopusscopus
Issue Date
2017
Journal Title
Canadian Journal of Mathematics
ISSN
0008-414XJCR Link
Citation
vol. 69, no. 3, pp. 579 - 594
Keywords
Class numberFunction fieldQuartic extensionRegulator
Publisher
Canadian Mathematical Society
Indexed
SCI; SCIE; SCOPUS WOS scopus
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
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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