The discrepancy of some real sequences
DOI:
https://doi.org/10.7146/math.scand.a-14423Abstract
Let (λn)n≥0 be a sequence of real numbers such that there exists δ>0 such that |λn+1−λn|≥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},⋯,{λN−1x}. 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.Downloads
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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