Quadratic algebraic numbers with finite  b ‐adic expansion on the unit circle and their distribution | Zendy

Dorfer Gerhard | Zendy; Tichy Robert F. | Zendy

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Quadratic algebraic numbers with finite b ‐adic expansion on the unit circle and their distribution

Author(s) -

Dorfer Gerhard,

Tichy Robert F.

Publication year - 2004

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200310196

Subject(s) - mathematics , unit circle , unit (ring theory) , quadratic equation , combinatorics , norm (philosophy) , integer (computer science) , algebraic number , sequence (biology) , distribution (mathematics) , quadratic integer , quadratic field , quadratic function , mathematical analysis , geometry , mathematics education , biology , political science , computer science , law , genetics , programming language

We consider elements x + y $ \sqrt {-m} $ in the imaginary quadratic number field ℚ( $ \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 full description of this set is given. Ordered by the number of digits in the b –adic expansion of the coordinates, the corresponding sequence of points on the unit circle, if infinite, is uniformly distributed. This continues work of P. Schatte who treated the case m = 1. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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