FourÄ±er coeffÄ±cÄ±ents of a class of ETA quotÄ±ents of weÄ±ght 20 wÄ±th level 12 - Kendirli, BarÄ±ÅŸ (International Journal of Advanced Mathematical Sciences, 2015)
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 Ïƒ(n),Ïƒ((n/2)),Ïƒ((n/3)) and Ïƒ((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 Ïƒâ‚ƒ(n),Ïƒâ‚ƒ((n/2)),Ïƒâ‚ƒ((n/3)) and Ïƒâ‚ƒ((n/6)).Here, we will express the even Fourier coefficients of 570 eta quotients in terms of Ïƒâ‚â‚‰(n),Ïƒâ‚â‚‰((n/2)),Ïƒâ‚â‚‰((n/3)),Ïƒâ‚â‚‰((n/4)),Ïƒâ‚â‚‰((n/6)) and Ïƒâ‚â‚‰((n/(12))).