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- 2015
Four?er coeff?c?ents of a class of ETA quot?ents of we?ght 20 w?th level 12Abstract: Williams and later Yao, Xia and Jin 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 σ?(n),σ?((n/2)),σ?((n/3)) and σ?((n/6)).Here, we will express the even Fourier coefficients of 570 eta quotients in terms of σ??(n),σ??((n/2)),σ??((n/3)),σ??((n/4)),σ??((n/6)) and σ??((n/(12))).
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