Fourier Coefficients of a Class of Eta Quotients of Weight 14 with Level 12
PDF

Keywords

 Dedekind eta function, eta quotients, Fourier series.

How to Cite

Barış Kendirli. (2015). Fourier Coefficients of a Class of Eta Quotients of Weight 14 with Level 12. Journal of Basic & Applied Sciences, 11, 454–483. https://doi.org/10.6000/1927-5129.2015.11.64

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

https://doi.org/10.6000/1927-5129.2015.11.64
PDF

References

Williams KS. Fourier series of a class of eta quotients. Int J Number Theory 2012; 8: 993-1004. http://dx.doi.org/10.1142/S1793042112500595

Yao OXM, Xia EXW, Jin J. Explicit Formulas for the Fourier coefficients of a class of eta quotients. Int J Number Theory 2013; 9(2): 487-503. http://dx.doi.org/10.1142/S179304211250145X

Köhler G. Eta Products and Theta Series Identities (Springer-Verlag, Berlin, 2011). http://dx.doi.org/10.1007/978-3-642-16152-0

Gordon B. Some identities in combinatorial analysis. Quart J Math Oxford Ser 1961; 12: 285-290.

Kac VG. Infinite-dimensional algebras, Dedekind’s ?-function, classical Möbius function and the very strange formula. Adv Math 1978; 30: 85-136. http://dx.doi.org/10.1016/0001-8708(78)90033-6

Macdonald IG. Affine root systems and Dedekind’s ?-function. Invent Math 1972; 15: 91-143. http://dx.doi.org/10.1007/BF01418931

Zucker IJ. A systematic way of converting infinite series into infinite products. J Phys A 1987; 20: L13-L17. http://dx.doi.org/10.1088/0305-4470/20/1/003

Zucker IJ. Further relations amongst infinite series and products: II. The evaluation of three-dimensional lattice sums. J Phys A 1990; 23: 117-132. http://dx.doi.org/10.1088/0305-4470/23/2/009

Kendirli B. Evaluation of Some Convolution Sums by Quasimodular Forms. Eur J Pure Appl Math 2015; 8(1): 81-110.

Kendirli B. Evaluation of Some Convolution Sums and Representation Numbers of Quadratic Forms of Discriminant 135. Br J Math Comp Sci 2015; 6(6): 494-531.

Kendirli B. Evaluation of Some Convolution Sums andthe Representation numbers. Ars Combinatorica CXVI: July, pp. 65-91.

Kendirli B. Cusp Forms in S4(?0(79)) and the number of representations of positive integers by some direct sum of binary quadratic forms with discriminant-79. Bull Korean Math Soc 2012; 49(3). http://dx.doi.org/10.4134/BKMS.2012.49.3.529

Kendirli B. Cusp Forms in S4(?0(47)) and the number of representations of positive integers by some direct sum of binary quadratic forms with discriminant -47, Hindawi. Int J Math Math Sci 2012; 303492 10 pages.

Kendirli B. The Bases of M4(?0(71)), M6(?0(71)) and the Number of Representations of Integers, Hindawi. Math Probl Eng 2013; 695265, 34 pages.

Alaca A, Alaca S, Williams KS. On the two-dimensional theta functions of Borweins. Acta Arith 2006; 124: 177-195. http://dx.doi.org/10.4064/aa124-2-4

Alaca A, Alaca S, Williams KS. Evaluation of the convolution sums ?l+12m=n ?(l)?(m) and ?3l+4m=n ?(l)?(m). Adv Theor Appl Math 2006; 1: 27-48.

Gordon B, Robins S. Lacunarity of Dedekind ?-products. Glasgow Math J 1995; 37: 1-14. http://dx.doi.org/10.1017/S0017089500030329

Diamond F, Shurman J. A First Course in Modular Forms. Springer Graduate Texts in Mathematics 228.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2015 Journal of Basic & Applied Sciences