Upper Bounds for Double Exponential Sums Along a Subsequence

White, Christopher J.

doi:10.1515/udt-2017-0012

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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Upper Bounds for Double Exponential Sums Along a Subsequence

Abstract

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