Journal of the Ramanujan Mathematical Society
Volume 31, Issue 1, March 2016 pp. 95–107.
Transcendence of certain Fourier series
Authors:
Chester Weatherby
Author institution:Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada
Summary:
In this note we offer and alternate approach to studying the
transcendental nature of the sums
∑ n ∈ Z f(n)A(n)/B(n) and
∑ n ∈ Z 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].
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