Fourier Coefficients of a Class of Eta Quotients of Weight 14 with Level 12 Pages 454-483

Fourier Coefficients of a Class of Eta Quotients of Weight 14 with Level 12
Pages 454-483
Barış Kendirli

DOI: http://dx.doi.org/10.6000/1927-5129.2015.11.64

Published: 19 August 2015

Abstract:  Recently, Williams [1] and then Yao, Xia and Jin [2] 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  and  and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of  and  . Here, by using the method of proof of Williams, we will express the even Fourier coefficients of 196 eta quotients i.e., the Fourier coefficients of the sum, f(q)+f(-q), of 196 eta quotients in terms of  and .

Keywords: Dedekind eta function, eta quotients, Fourier series.