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Periodic elements and number systems in Q(√2)

✍ Scribed by G. Farkas

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
442 KB
Volume
38
Category
Article
ISSN
0895-7177

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✦ Synopsis

Let us consider an arbitrary quadratic extension of the field of rational numbers Our prospective purpose is to give for an arbitrary algebraic integer a, if any, such a digit set. that constitutes a number system with cr. In this paper, we deal with the periodic elements of systems given in Q(a)

and prove that either the modulus of them or that of their conjugate is less than 1. On the basis of this result, we hope that there exists some algorithm which provides number systems.

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