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Upper bounds for certain trigonometric sums involving cosine powers

Volume 141 / 2015

Anastasios D. Simalarides 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.

Authors

  • Anastasios D. Simalarides196 Kifissias Street
    Kifissia 14562, Attica, Greece
    e-mail

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