Index Form Equations in General

István Gaál
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István Gaál: University of Debrecen, Institute of Mathematics and Informatics

Chapter 4 in Diophantine Equations and Power Integral Bases, 2002, pp 45-52 from Springer

Abstract: Abstract In this chapter we investigate the structure of the index form (1.1). Discovering special properties of the index form, especially factorization properties, makes the resolution of index form equations much easier. A special situation (which otherwise is frequent in numerical examples) is considered in Section 4.4, when the field K is the composite of its subfields. The general results on composite fields have several applications, see e.g., Sections 8.3, 10.2, 10.3.1 and 10.3.3.

Keywords: Number Field; Diophantine Equation; Index Form; Algebraic Integer; Integral Basis (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4612-0085-7_4

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