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arXiv · 1510.07983

Upper bounds for double exponential sums along a subsequence

Christopher J. White
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Abstract

We consider a class of double exponential sums studied in a paper of Sinai and Ulcigrai. They proved a linear bound for these sums along the sequence of denominators in the continued fraction expansion of $α$, provided $α$ is badly-approximable. We provide a proof of a result, which includes a simple proof of their theorem, and which applies for all irrational $α$.

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Christopher J. White. 2015-10-27. Upper bounds for double exponential sums along a subsequence. https://arxiv.org/abs/1510.07983

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