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 ...

For a power series $f(z) = \sum^\infty_{k = 0} a_kz^k$ let $S_n(f)$ denote the maximum modulus of the zeros of the $n$th partial sum of $f$ and let $r_n(f)$ denote ...