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 1 and 2 and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of 3 and 4 . 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 5 and 6.

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