1. Well-Rounded ideal lattices of cyclic cubic and quartic fields
- Author
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Tran, Dat T., Le, Nam H., and Tran, Ha T. N.
- Subjects
Mathematics - Number Theory ,11R16, 06B10, 06B99, 11Y40 - Abstract
In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded ideal. We also prove that there exist families of cyclic quartic fields which have well-rounded ideals and explicitly construct their minimal bases. In addition, for a given prime number $p$, if a cyclic quartic field has a unique prime ideal above $p$, then we provide the necessary and sufficient conditions for that ideal to be well-rounded. Moreover, in cyclic quartic fields, we provide the prime decomposition of all odd prime numbers and construct an explicit integral basis for every prime ideal., Comment: 42 pages
- Published
- 2023
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