Determinations of Analogues of Gauss Sums and Other Trigonometric Sums

Matthias Beck, Bruce C. Berndt, O-Yeat Chan, Alexandru Zaharescu

Published 2005-04-07, updated 2005-08-01Version 2

Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated with primitive odd characters. In this paper, we establish two general theorems involving both sines and cosines, with more attention given to cosine sums in the several examples that we provide.