Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Samuel A. Hambleton"'
Autor:
Samuel A. Hambleton, Hugh C. Williams
The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equat
Autor:
Samuel A. Hambleton, Hugh C. Williams
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
The complete collection of cubic fields with a given fundamental discriminant can be constructed from certain algebraic integers in the associated quadratic resolvent field. Berwick explained how each such quadratic integer determines the roots of a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7294176a4585f8b81213db9708a3ebdd
https://doi.org/10.1007/978-3-030-01404-9_4
https://doi.org/10.1007/978-3-030-01404-9_4
Autor:
Samuel A. Hambleton, Hugh C. Williams
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
Binary cubic forms were a natural thing for Gauss’ student Eisenstein to consider after Gauss pioneered the study of classes of binary quadratic forms which lead to the understanding of the ideal class group. Eisenstein deduced some interesting res
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4d983360e78403efbeaa932311d99a27
https://doi.org/10.1007/978-3-030-01404-9_3
https://doi.org/10.1007/978-3-030-01404-9_3
Autor:
Hugh C. Williams, Samuel A. Hambleton
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
In this chapter we focus on the ideals of the maximal order. We also discuss the ideals of any order of \(\mathbb{K}\), the lattices over \(\mathbb{K}\), and the properties of 1-lattices over \(\mathbb{K}\). We define the ideal class group of \(\math
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e5b6000a6aa164a719c5175f1789249b
https://doi.org/10.1007/978-3-030-01404-9_2
https://doi.org/10.1007/978-3-030-01404-9_2
Autor:
Samuel A. Hambleton, Hugh C. Williams
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
The least positive integers such that there exist rational integers representing the absolute values of a reduced binary quadratic form and a reduced binary cubic form can be calculated by the simple continued fractions of a quadratic irrationality a
Externí odkaz:
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https://doi.org/10.1007/978-3-030-01404-9_6
https://doi.org/10.1007/978-3-030-01404-9_6
Autor:
Samuel A. Hambleton, Hugh C. Williams
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
For a quadratic field of discriminant D, the units of norm 1 are in one-to-one correspondence with the integer points of the equation X2 − DY2 = 4, often called the Pell equation. This makes it possible, as many throughout history have done, to stu
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https://doi.org/10.1007/978-3-030-01404-9_5
https://doi.org/10.1007/978-3-030-01404-9_5
Autor:
Hugh C. Williams, Samuel A. Hambleton
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
In this chapter we show how to find a particular type of basis, called a prepared basis, and derive some inequalities associated with this basis. Such a basis is essential for finding the relative minimum adjacent to 1 in a reduced lattice and a Voro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a5722b9e23712db4c427ba9d95fb25ad
https://doi.org/10.1007/978-3-030-01404-9_8
https://doi.org/10.1007/978-3-030-01404-9_8
Autor:
Samuel A. Hambleton, Hugh C. Williams
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::de528d0da451153bcc83d3261c4bcf0a
https://doi.org/10.1007/978-3-030-01404-9_1
https://doi.org/10.1007/978-3-030-01404-9_1
Autor:
Samuel A. Hambleton, Hugh C. Williams
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
In this chapter, we provide an overview of Voronoi’s continued fraction algorithm that forms the basis for finding the fundamental unit(s) of a cubic field. We begin with a discussion of how Voronoi extended the idea of a simple continued fraction
Externí odkaz:
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https://doi.org/10.1007/978-3-030-01404-9_7
https://doi.org/10.1007/978-3-030-01404-9_7
Autor:
Samuel A. Hambleton, Hugh C. Williams
Publikováno v:
CMS Books in Mathematics ISBN: 9783030014025
Choose any two rational numbers and get an element of norm 1 of a cubic field. We give formulas for doing this in terms of the generic letters a, b, c, d used to define the cubic field generated by the polynomial with these coefficients. This is rela
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https://doi.org/10.1007/978-3-030-01404-9_9
https://doi.org/10.1007/978-3-030-01404-9_9