Mathematical Notes

, Volume 78, Issue 3–4, pp 563–568

Linear and Algebraic Independence of q-Zeta Values

  • Yu. A. Pupyrev
Article

Abstract

In the paper, results on linear and algebraic independence of q-series of the form \(\varsigma _q (s) = \sum\nolimits_{n = 1}^\infty {\sigma _{s - 1} (n)q^n }\) over the field ℂ(q) are obtained, where \(\sigma _{s - 1} (n) = \sum\nolimits_{d|n} {d^{s - 1} }\), s = 1, 2,... .

Key words

Eisenstein series q-zeta value linear independence algebraic independence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    K. Mahler, “On algebraic differential equations satisfied by automorphic functions,” J. Austral. Math. Soc., 10 (1969), 445–450.Google Scholar
  2. 2.
    V. V. Zudilin, “Diophantine problems for q-zeta values,” Mat. Zametki [Math. Notes], 72 (2002), no. 6, 936–940.Google Scholar
  3. 3.
    Yu. V. Nesterenko, Transcendence of Some Functions [in Russian], Manuscript (2003).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Yu. A. Pupyrev
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations