2015/10/27 by Christopher J. White, White, Christopher J.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1510.07983
12 pages
arxiv created 2015/10/27 · arxiv updated 2015/10/28
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.