Transactions of the American Mathematical Society, Vol. 359, No. 3 (Mar., 2007), pp. 1161-1189 (29 pages) We consider sums of the form $\sum_{j=0}^{n-1}F_{1}(a_{1}n+b ...

Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...