Upper bounds for certain trigonometric sums involving cosine powers
Volume 141 / 2015
Colloquium Mathematicum 141 (2015), 249-260
MSC: Primary 11L03, 11L40; Secondary 42A05.
DOI: 10.4064/cm141-2-9
Abstract
We establish upper bounds for certain trigonometric sums involving cosine powers. Part of these results extend previous ones valid for the sum \[ \sum^{k-1}_{m=1}\frac{|\!\sin(\pi rm/k)|}{\sin(\pi m/k)}. \] We apply our results to estimate character sums in an explicit and elementary way.
