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On Inhomogeneous Diophantine Approximation

โœ Scribed by T.W. Cusick; A.M. Rockett; P. Szusz

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
714 KB
Volume
48
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and SwinnertonDyer. As an application, a new proof of a theorem of Davenport, which gives the complete sequence of inhomogeneous minima for the form (x^{2}-x y-y^{2}), is given. C) 1994 Academic Press, Inc.

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A modification of the Ford geometric approach to the problem of approximation of complex numbers by elements of an imaginary quadratic number field is developed. An upper bound for the Hurwitz constant for the field is obtained in terms of the geometry of the isometric fundamental domain for the cor