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A lower bound in the law of the iterated logarithm for general lacunary series

Volume 222 / 2014

Charles N. Moore, Xiaojing Zhang Studia Mathematica 222 (2014), 207-228 MSC: Primary 42A55; Secondary 60F15. DOI: 10.4064/sm222-3-2

Abstract

We prove a lower bound in a law of the iterated logarithm for sums of the form $\sum _{k=1}^N a_k f(n_k x+c_k)$ where $f$ satisfies certain conditions and the $n_k$ satisfy the Hadamard gap condition $n_{k+1}/n_k\geq q >1. $

Authors

  • Charles N. MooreDepartment of Mathematics
    Kansas State University
    Manhattan, KS 66506, U.S.A.
    and
    Department of Mathematics
    Washington State University
    Pullman, WA 99164, U.S.A.
    e-mail
    e-mail
  • Xiaojing ZhangDepartment of Mathematics
    Kansas State University
    Manhattan, KS 66506, U.S.A.
    e-mail

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