Fourier Coefficients of a Class of Eta Quotients of Weight 18 with Level 12
Pure and Applied Mathematics Journal
Volume 4, Issue 4, August 2015, Pages: 178-188
Received: Jun. 20, 2015; Accepted: Aug. 4, 2015; Published: Aug. 12, 2015
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Author
Baris Kendirli, Dept. of Math,. Aydın University, Istanbul, Turkey
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Abstract
Williams [16] and later 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 σ_3 (n),σ_3 (n/2),σ_3 (n/3) and σ_3 (n/6). Here, we will express the even Fourier coefficients of 324 eta quotients in terms of σ_17 (n),σ_17 (n/2),σ_17 (n/3),σ_17 (n/4),σ_17 (n/6) and σ_17 (n/12).
Keywords
Dedekind Eta Function, Eta Quotients, Fourier Series
To cite this article
Baris Kendirli, Fourier Coefficients of a Class of Eta Quotients of Weight 18 with Level 12, Pure and Applied Mathematics Journal. Vol. 4, No. 4, 2015, pp. 178-188. doi: 10.11648/j.pamj.20150404.17
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