Algebraic independence results for the sixteen families of q-series

Carsten Elsner, Shun Shimomura, Iekata Shiokawa, Yohei Tachiya

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The sixteen families of q-series containing the Ramanujan functions were listed by I.J. Zucker (SIAM J. Math. Anal. 10:192-206, 1979), which are generated from the Fourier series expansions of the Jacobian elliptic functions or some of their squares. This paper discusses algebraic independence properties for these q-series. We determine all the sets of q-series such that, at each algebraic point, the values of the q-series in the set are algebraically independent over ℚ. We also present several algebraic relations over ℚ for two or three of these q-series.

Original languageEnglish
Pages (from-to)315-344
Number of pages30
JournalRamanujan Journal
Volume22
Issue number3
DOIs
Publication statusPublished - 2010

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Independence Results
Algebraic Independence
Q-series
Jacobian Elliptic Function
Fourier Expansion
Ramanujan
Series Expansion
Fourier series
Family

Keywords

  • Algebraic independence
  • Jacobian elliptic functions
  • Nesterenko's theorem
  • q-series
  • Ramanujan functions

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Algebraic independence results for the sixteen families of q-series. / Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata; Tachiya, Yohei.

In: Ramanujan Journal, Vol. 22, No. 3, 2010, p. 315-344.

Research output: Contribution to journalArticle

Elsner, C, Shimomura, S, Shiokawa, I & Tachiya, Y 2010, 'Algebraic independence results for the sixteen families of q-series', Ramanujan Journal, vol. 22, no. 3, pp. 315-344. https://doi.org/10.1007/s11139-010-9235-4
Elsner, Carsten ; Shimomura, Shun ; Shiokawa, Iekata ; Tachiya, Yohei. / Algebraic independence results for the sixteen families of q-series. In: Ramanujan Journal. 2010 ; Vol. 22, No. 3. pp. 315-344.
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