Fourier coefficients of a class of eta quotients of weight 10

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).