Abstract
In this chapter we shall require some knowledge about algebraic number fields. Throughout, K will be an algebraic number field of degree k, and ℜ will denote the norm from K to the field ℚ of rationals. There are k isomorphic embeddings ϕ1,...,ϕk, of K into the complex numbers; denote the image of an element α of K under ϕi by ϕ(i). We will always tacitly assume that ϕ1, is the identity map, so that α (1) = α, and we shall say that α (1) = α, α (2),...α (k) are the conjugates of α. In this notation ℜ(α) = α (1)...α (k). Given a linear form
with coefficients in K we write
Keywords
- Linear Form
- Finite Index
- Real Form
- Primitive Element
- Integer Point
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References
Z.I. Borevich and I.R. Shafarevich (1966). Number Theory. (Translated from the Russian). Academic Press.
W.M. Schmidt (1971c). Linearformen mit algebraischen Koeffizienten. II. Math. Ann. 191, 1–20.
____ (1972). Norm form equations. Ann. of Math. 96, 526–551.
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© 1980 Springer-Verlag Berlin Heidelberg
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(1980). Norm Form Equations. In: Diophantine Approximation. Lecture Notes in Mathematics, vol 785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38645-2_7
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DOI: https://doi.org/10.1007/978-3-540-38645-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09762-4
Online ISBN: 978-3-540-38645-2
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