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