噱头
发表于 2025-3-27 00:33:17
Cubic Pell Equations,is chapter, we derive several Diophantine equations associated with a cubic field, investigate relationships between them, derive their group laws, briefly discuss points modulo a prime, and consider naive algorithms for solving some of these Diophantine equations.
燕麦
发表于 2025-3-27 04:23:56
,Voronoi’s Theory of Continued Fractions,ermination of the fundamental unit of a cubic field of negative discriminant or of a fundamental pair of units of a cubic field of positive discriminant. These problems reduce to the task of finding a particular relative minimum adjacent to 1 in a reduced lattice which we will discuss in the next chapter.
向宇宙
发表于 2025-3-27 07:17:29
Cubic Fields,e of arithmetic in these structures. We also discuss the various types of cubic fields and the properties of the units and regulator. We conclude with a collection of results concerning the development of the simple continued fraction of a cubic irrationality.
绝种
发表于 2025-3-27 10:16:13
Relative Minima Adjacent to 1 in a Reduced Lattice,in various parts of the overall algorithm. We present an algorithm for finding a reduced lattice similar to a given one, and conclude with some useful connections between prepared bases and binary cubic forms.
固执点好
发表于 2025-3-27 16:19:42
Parametrization of Norm 1 Elements of ,, discuss this work with very little of the language or tools of algebraic geometry, with the exception of some projective geometry. We also discuss conics and singular elliptic curves as they are significantly easier to parameterize.
ACE-inhibitor
发表于 2025-3-27 20:51:35
Cubic Ideals and Lattices, any non-zero ideal of . can be represented uniquely as the product of prime ideals. We conclude with a review of the analytic class number formula and exhibit several results relating the class number of the cubic field to its regulator.
暂停,间歇
发表于 2025-3-27 22:41:39
‘Anglo-America’ and Atlantic Europee of arithmetic in these structures. We also discuss the various types of cubic fields and the properties of the units and regulator. We conclude with a collection of results concerning the development of the simple continued fraction of a cubic irrationality.
Epithelium
发表于 2025-3-28 03:08:04
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使腐烂
发表于 2025-3-28 07:22:07
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Mirage
发表于 2025-3-28 12:53:38
David Courpasson,Jean-Claude Thoenign of Shanks’ method due toFung found generating polynomials of all 364 cubic fields with a 19-digit discriminant. This chapter presents the never before published Shanks-Fung algorithm and, for completeness, concludes with a brief summary ofBelabas’ fast technique for tabulating all cubic fields of bounded discriminant.