A remark on Nesterenko's theorem for Ramanujan functions

Carsten Elsner, Shun Shimomura, Iekata Shiokawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 A1(q), A2i+1(q), A2j+1(q) are algebraically independent over. Furthermore, the q-series A2i+1(q) and A2j+1(q) are algebraically dependent over if and only if (i, j)=(1, 3).

Original languageEnglish
Pages (from-to)211-221
Number of pages11
JournalRamanujan Journal
Volume21
Issue number2
DOIs
Publication statusPublished - 2010 Jan

Fingerprint

Q-series
Ramanujan
Algebraic Independence
Theorem
If and only if
Distinct
Integer
Dependent

Keywords

  • Algebraic independence
  • Nesterenko's theorem
  • Ramanujan functions

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

A remark on Nesterenko's theorem for Ramanujan functions. / Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata.

In: Ramanujan Journal, Vol. 21, No. 2, 01.2010, p. 211-221.

Research output: Contribution to journalArticle

Elsner, C, Shimomura, S & Shiokawa, I 2010, 'A remark on Nesterenko's theorem for Ramanujan functions', Ramanujan Journal, vol. 21, no. 2, pp. 211-221. https://doi.org/10.1007/s11139-009-9163-3
Elsner, Carsten ; Shimomura, Shun ; Shiokawa, Iekata. / A remark on Nesterenko's theorem for Ramanujan functions. In: Ramanujan Journal. 2010 ; Vol. 21, No. 2. pp. 211-221.
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