Fourier Coefficients of a Class of Eta Quotients of Weight 16 with Level 12

Barış  Kendirli

doi:10.4236/am.2015.68133

Barış Kendirli

Abstract: Recently, Williams [1] and then Yao, Xia and Jin [2] 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 and and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of and . Here, by using the method of proof of Williams, we will express the even Fourier coefficients of 360 eta quotients i.e., the Fourier coefficients of the sum, f(q) + f(?q), of 360 eta quotients in terms of and .

Keywords: Dedekind Eta Function, Eta Quotients, Fourier Series

Cite this paper: Kendirli, B. (2015) Fourier Coefficients of a Class of Eta Quotients of Weight 16 with Level 12. Applied Mathematics, 6, 1426-1493. doi: 10.4236/am.2015.68133.

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