Skip to content
Research Article Open access CC BY 4.0

Fourier Coefficients of A Class of Eta Quotients of Weight 6

Barış Kendirli

Journal of Advances in Mathematics and Computer Science · pp. 1–19 · Published 13 Apr 2016

10.9734/BJMCS/2016/24665

Abstract

Recently,Williams expressed all coefficients of one hundred and twenty-six eta quotients in terms of σ(n), σ(n/2), σ(n/3) and σ(n/6), and Yao, Xia and Jin, expressed only even coefficients of one hundred and four eta quotients in terms of σ3(n), σ3(n/2), σ3(n/3) and σ3(n/6). The Fourier series expansions of a class of eta quotients in terms of σk-1(n), σk-1(n/2), σk-1(n/3) and σk-1(n/6) for k = 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 have been expressed by the author. The Fourier series expansions of a class of eta quotients in M2 (Γ0, χ) in terms of σ(n), σ(n/2), σ(n/3) and σ(n/6) has been found by Alaca and the Fourier series expansions of a class of eta quotients in M4 (Γ0, χ) in terms of σ3(n), σ3(n/2), σ3(n/3) and σ3(n/6) has been determined by the author. Here, we will determine the coefficients of the Fourier series expansions of a class of eta quotients in M6 (Γ0, χ) in terms of σ5(n), σ5(n/2), σ5(n/3), σ5(n/6) and Fourier coefficients of the eight eta quotients.

Fourier series Dedekind eta function Eta quotients.

References (20)

  1. 1 The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and 𝑞-series [DOI]
  2. 2 Affine root systems and Dedekind's?-function [DOI]
  3. 3 Eta Products and Theta Series Identities [DOI]
  4. 4 Infinite-dimensional algebras, Dedekind's η-function, classical möbius function and the very strange formula [DOI]
  5. 5 FOURIER SERIES OF A CLASS OF ETA QUOTIENTS [DOI]
  6. 6 EXPLICIT FORMULAS FOR THE FOURIER COEFFICIENTS OF A CLASS OF ETA QUOTIENTS [DOI]
  7. 7 Evaluation of Some Convolution Sums and Representation Numbers of Quadratic Forms of Discriminant -135 [DOI]
  8. 8 SOME IDENTITIES IN COMBINATORIAL ANALYSIS [DOI]
  9. 9 Further relations amongst infinite series and products. II. The evaluation of three-dimensional lattice sums [DOI]
  10. 10 A systematic way of converting infinite series into infinite products [DOI]
  11. 11 CUSP FORMS IN S4(Γ0(79)) AND THE NUMBER OF REPRESENTATIONS OF POSITIVE INTEGERS BY SOME DIRECT SUM OF BINARY QUADRATIC FORMS WITH DISCRIMINANT -79 [DOI]
  12. 12 Cusp Forms in and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant [DOI]
  13. 13 Lacunarity of Dedekind η-products [DOI]
  14. 14 Fourier Coefficients of a Class of Eta Quotients of Weight 18 with Level 12 [DOI]
  15. 15 Fourier Coefficients of some Eta Quotients of Weight 8
  16. 16 Fourier Coefficients of a Class of Eta Quotients of Weight 12 with Level 12 [DOI]
  17. 17 Fourıer coeffıcıents of a class of ETA quotıents of weıght 20 wıth level 12 [DOI]
  18. 18 Fourier Coefficients of a Class of Eta Quotients of Weight 12 [DOI]
  19. 19 Fourier Coefficients of a Class of Eta Quotients [DOI]
  20. 20 Fourier Coefficients of a Class of Eta Quotients of Weight 4 [DOI]

Cited by 1

Fourier Coefficients of a Class of Eta Quotients of Weight 4

B. Kendirli · 2016

Related research

Article metrics

Real usage data collected on this platform.

0

Page views

0

PDF downloads

0

Outbound clicks

1

Citations

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

No views recorded yet.

Traffic sources

Referring site, by host.

No traffic recorded yet.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.