Algebraic independence results for the sixteen families of q-series

Carsten Elsner, Shun Shimomura, Iekata Shiokawa, Yohei Tachiya

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)315-344
ページ数30
ジャーナルRamanujan Journal
22
3
DOI
出版ステータスPublished - 2010 4 29

ASJC Scopus subject areas

  • 代数と数論

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