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ON THE DISCREPANCY OF THE SEQUENCE (α√n)

Published online by Cambridge University Press:  01 June 1998

C. BAXA  and
J. SCHOISSENGEIER
C. BAXA
Affiliation:
Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria. E-mail: [email protected]
J. SCHOISSENGEIER
Affiliation:
Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria. E-mail: [email protected]
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Abstract

The first person to consider the discrepancy of sequences of the type (αnσ)n[ges ]1 (where 0<σ<1) was H. Behnke. The subject was taken up again by one of the authors of this paper, who gave a detailed description of the discrepancy's behaviour if either 0<σ<½ or σ=½ and α2∉ℚ or σ=½ and α−2∈ℕ. In this paper, we study the case of sequences (α√n)n[ges ]1 where α>0 and α2∈ℚ. Both

formula here

are expressed as maxima of finitely many numbers which involve class numbers of imaginary quadratic fields in many cases.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 529 - 544
Copyright
The London Mathematical Society 1998

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