The discrepancy of some real sequences

Authors

  • H. Kamarul Haili
  • R. Nair

DOI:

https://doi.org/10.7146/math.scand.a-14423

Abstract

Let (λn)n0 be a sequence of real numbers such that there exists δ>0 such that |λn+1λn|δ,n=0,1,.... For a real number y let {y} denote its fractional part. Also, for the real number x let D(N,x) denote the discrepancy of the numbers {λ0x},,{λN1x}. We show that given ε>0, 9774 D(N,x) = o ( N^{-\frac{1}{2}}(\log N)^{\frac{3}{2} + \varepsilon})9774 almost everywhere with respect to Lebesgue measure.

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Published

2003-12-01

How to Cite

Haili, H. K., & Nair, R. (2003). The discrepancy of some real sequences. MATHEMATICA SCANDINAVICA, 93(2), 268–274. https://doi.org/10.7146/math.scand.a-14423

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Articles