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On approximation of -adic numbers by -adic algebraic numbers

✍ Scribed by V.V. Beresnevich; V.I. Bernik; E.I. Kovalevskaya

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
319 KB
Volume
111
Category
Article
ISSN
0022-314X

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## Abstract We consider elements __x__ + __y__$ \sqrt {-m} $ in the imaginary quadratic number field β„š($ \sqrt {-m} $) such that the norm __x__^2^ + __my__^2^ = 1 and both __x__ and __y__ have a finite __b__–adic expansion for an arbitrary but fixed integer base __b__. For __m__ = 2, 3, 7 and 11 a