# Journal of the Ramanujan Mathematical Society

Volume 28, Issue 1, March 2013 pp. 113--139.

Transcendence of series of rational functions and a problem of Bundschuh**Authors**: Chester Weatherby

**Author institution:**Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6

**Summary:**We investigate the transcendental nature of the sums

*A*where

*A*(

*x*),

*B*(

*x*) is an algebraic valued periodic function, and the sum is over integers

*n*which are not zeros of

*B*(

*x*). We offer a new method of evaluating these sums using only elementary techniques. In some cases we relate these sums to a celebrated theorem of Nesterenko and a conjecture of Schneider and obtain concrete as well as conditional transcendence results. These results include progress on a problem of Bundschuh regarding the sum for integer values of

*s*.

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