A remark on Nesterenko's theorem for Ramanujan functions

Carsten Elsner, Shun Shimomura, Iekata Shiokawa

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5 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2010 Jan


  • Algebraic independence
  • Nesterenko's theorem
  • Ramanujan functions

ASJC Scopus subject areas

  • Algebra and Number Theory


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