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- W2904534303 abstract "Let $(n_k)_{k=1}^{infty}$ be a lacunary sequence of integers. We show that if $mu$ is a probability measure on $[0,1)$ such that $|widehat{mu}(t)|leq c|t|^{-eta}$, then for $mu$-almost all $x$, the discrepancy $D_N(n_kx)$ satisfies begin{equation*} frac{1}{4} leq limsup_{Ntoinfty}frac{N D_N(n_kx)}{sqrt{Nloglog N}} leq C end{equation*} for some constant $C>0$, proving a conjecture of Haynes, Jensen and Kristensen. This allows a slight improvement on their previous result on products of the form $q|qalpha| |qbeta-gamma| $." @default.
- W2904534303 created "2018-12-22" @default.
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- W2904534303 date "2018-12-15" @default.
- W2904534303 modified "2023-09-27" @default.
- W2904534303 title "The discrepancy of $(n_kx)$ with respect to certain probability measures" @default.
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