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Construction of all cubic function fields of a given square-free discriminant

Title
Construction of all cubic function fields of a given square-free discriminant
Authors
Jacobson, M. J., Jr.Lee, Y.Scheidler, R.Williams, H. C.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2015
Journal Title
INTERNATIONAL JOURNAL OF NUMBER THEORY
ISSN
1793-0421JCR Link1793-7310JCR Link
Citation
vol. 11, no. 6, pp. 1839 - 1885
Keywords
Cubic function fieldquadratic function fielddiscriminantsignaturequadratic generatorreduced ideal
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Indexed
SCIE; SCOPUS WOS scopus
Abstract
For any square-free polynomial D over a finite field of characteristic at least 5, we present an algorithm for generating all cubic function fields of discriminant D. We also provide a count of all these fields according to their splitting at infinity. When D' = D/(-3) has even degree and a leading coefficient that is a square, i.e. D' is the discriminant of a real quadratic function field, this method makes use of the infrastructures of this field. This infrastructure method was first proposed by Shanks for cubic number fields in an unpublished manuscript from the late 1980s. While the mathematical ingredients of our construction are largely classical, our algorithm has the major computational advantage of finding very small minimal polynomials for the fields in question.
DOI
10.1142/S1793042115500803
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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