Titlebook: Cubic Fields with Geometry; Samuel A. Hambleton,Hugh C. Williams Book 2018 Springer Nature Switzerland AG 2018 binary cubic forms.cubic fi

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Springer Nature Switzerland AG 2018

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‘Anglo-America’ and Atlantic Europeany of the well-known properties of these numbers. In particular, we describe the cubic polynomial and develop many of the attributes of the cubic field generated by such a polynomial. This involves examining orders, the maximal order, integral bases of an order, the discriminant, and the performanc

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David Courpasson,Jean-Claude Thoenig1-lattices over .. We define the ideal class group of . and the class number of .. We next examine the prime ideals in the maximal order and show that 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 an

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David Courpasson,Jean-Claude Thoenig which lead to the understanding of the ideal class group. Eisenstein deduced some interesting results on binary cubic forms. While those results were mostly concerned with composition, binary cubic forms are much more generally important in the study of cubic fields. Binary cubic forms are an essen

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Introduction: Illuminating a Twilight Worldfield. We begin with a discussion of how Voronoi extended the idea of a simple continued fraction of a quadratic irrationality to that of a cubic irrationality. Next, we provide an account of relative minima in cubic lattices, reduced lattices (lattices in which 1 is a relative minimum), and chains

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