Upper bounds for certain trigonometric sums involving cosine powers

Anastasios D. Simalarides

Colloquium Mathematicae, Tome 139 (2015), p. 249-260 / Harvested from The Polish Digital Mathematics Library

Résumé

We establish upper bounds for certain trigonometric sums involving cosine powers. Part of these results extend previous ones valid for the sum $\sum_{m = 1}^{k - 1} | s i n (π r m / k) | / s i n (π m / k)$ . We apply our results to estimate character sums in an explicit and elementary way.

Publié le : 2015-01-01

Zbl 06487242

EUDML-ID : urn:eudml:doc:284275

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     title = {Upper bounds for certain trigonometric sums involving cosine powers},
     journal = {Colloquium Mathematicae},
     volume = {139},
     year = {2015},
     pages = {249-260},
     zbl = {06487242},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-9}
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Anastasios D. Simalarides. Upper bounds for certain trigonometric sums involving cosine powers. Colloquium Mathematicae, Tome 139 (2015) pp. 249-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-9/