Fourier Coefficients of some Eta Quotients of Weight 8

Abstract

Recently, Williams and then Yao, Xia, Jin yao discovered the explicit formulas of the coefficients of 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)),σ((n/6)) and Yao, Xia, Jin expressed only even coefficients of 104 eta quotients in terms of σ₃(n),σ₃((n/2)),σ₃((n/3)),σ₃((n/6)).Here, we will express the odd Fourier coefficients of 64 eta quotients in terms of σ₇(2n-1),σ₇(((2n-1)/3)) and even Fourier coefficients of 130 eta quotients in terms of σ₇(n),σ₇((n/2)),σ₇((n/3)),σ₇((n/4)),σ₇((n/6)),σ₇((n/(12))).