View : 265 Download: 0
Construction of all cubic function fields of a given square-free discriminant
- Construction of all cubic function fields of a given square-free discriminant
- Jacobson, M. J., Jr.; Lee, Y.; Scheidler, R.; Williams, H. C.
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- INTERNATIONAL JOURNAL OF NUMBER THEORY
- INTERNATIONAL JOURNAL OF NUMBER THEORY vol. 11, no. 6, pp. 1839 - 1885
- Cubic function field; quadratic function field; discriminant; signature; quadratic generator; reduced ideal
- WORLD SCIENTIFIC PUBL CO PTE LTD
- SCIE; SCOPUS
- Document Type
Show the fulltext
- 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 This infrastructure method was first proposed by Shanks for cubic number fields in an unpublished manuscript from the late 1980s.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.
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
- Files in This Item:
There are no files associated with this item.
- RIS (EndNote)
- XLS (Excel)
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.