Journal of the Ramanujan Mathematical Society

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Transcendence of Certain Fourier Series


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1 Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada
     

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In this note we offer and alternate approach to studying the transcendental nature of the sums

Σ 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].


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  • Transcendence of Certain Fourier Series

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Authors

Chester Weatherby
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Abstract


In this note we offer and alternate approach to studying the transcendental nature of the sums

Σ 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].