### Abstract

We study the algebraic independence of values of the Ramanujan q-series. It is proved that, for any distinct positive integers i, j satisfying (i, j)≠(1, 3) and for any with 0<{pipe}q{pipe}<1, the numbers A_{1}(q), A_{2i+1}(q), A_{2j+1}(q) are algebraically independent over. Furthermore, the q-series A_{2i+1}(q) and A_{2j+1}(q) are algebraically dependent over if and only if (i, j)=(1, 3).

Original language | English |
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Pages (from-to) | 211-221 |

Number of pages | 11 |

Journal | Ramanujan Journal |

Volume | 21 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2010 Jan 1 |

### Keywords

- Algebraic independence
- Nesterenko's theorem
- Ramanujan functions

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Elsner, C., Shimomura, S., & Shiokawa, I. (2010). A remark on Nesterenko's theorem for Ramanujan functions.

*Ramanujan Journal*,*21*(2), 211-221. https://doi.org/10.1007/s11139-009-9163-3