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Published online by Cambridge University Press: 01 June 1998
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.
