Fourıer coeffıcıents of a class of ETA quotıents of weıght 20 wıth level 12

Abstract

<p>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 σ₃(n),σ₃((n/2)),σ₃((n/3)) and σ₃((n/6)).Here, we will express the even Fourier coefficients of 570 eta quotients in terms of σ₁₉(n),σ₁₉((n/2)),σ₁₉((n/3)),σ₁₉((n/4)),σ₁₉((n/6)) and σ₁₉((n/(12))).</p>

Fourier Coefficients of a Class of Eta Quotients of Weight 4

“…Motivated by these two results, we find that we can express the even and odd coefficients of the Fourier series expansions of a class of eta quotients in terms of σ k−1 (n), σ k−1 ( [22],20 [23],22 [24],24 [25]. Meanwhile, Alaca [26] has obtained the coefficients of the Fourier series expansions of a class of eta quotients in M 2 (Γ 0 , χ) in terms of σ(n), σ( ).…”

Fourier Coefficients of A Class of Eta Quotients of Weight 6

“…) for k = 6 [16],8 [17], 10[18],12 [19],14 [20],16 [21], 18 [22],20 [23],22 [24],24 [25]. Meanwhile, Alaca [26] has obtained the coefficients of the Fourier series expansions of a class of eta quotients in M 2 (Γ 0 , χ) in terms of σ(n), σ( ).…”