Fourier coefficients of a class of eta quotients of weight 10

Barış Kendirli

Abstract


Recently, Williams [18] and Yao, Xia and Jin[15] discovered explicit formulas for the coefficients of the Fourier series expansions of a class of eta quotients. Williams expressed all coefficients of 126 eta quotients in terms of σ(n), σ(n/2), σ(n/3) and σ(n/6) and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of σ3(n), σ3(n/2), σ3(n/3) and σ3(n/6). Here, by using the method of proof of Williams, we will express the even Fourier coefficients of 100 eta quotients i.e., the Fourier coefficients of the sum, f(q)+f(-q), of 100 eta quotients in terms of σ9(n), σ9(n/2), σ9(n/3), σ9(n/4), σ9(n/6), σ9(n/12).

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How to Cite this Article:

Barış Kendirli, Fourier coefficients of a class of eta quotients of weight 10, Journal of Mathematical and Computational Science, Vol 5, No 6 (2015), 780-810

Copyright © 2015 Barış Kendirli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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