Transcendence of Certain Fourier Series

Abstract

In this note we offer and alternate approach to studying the transcendental nature of the sumsΣ f(n)A(n)/B(n) and Σ A(n)/B(n)where A(x), B(x) are polynomials with algebraic coefficients with deg A < deg B, f is an algebraic valued periodic function, and the sum is over integers n which are not zeros of B(x). By relating these sums to the Fourier series of certain functions we are able to obtain an alternate formulation of some results found in [3] and [6].