Mathematical Notes

, Volume 78, Issue 3, pp 563–568

Linear and Algebraic Independence of q-Zeta Values

  • Yu. A. Pupyrev
Article

DOI: 10.1007/s11006-005-0155-3

Cite this article as:
Pupyrev, Y.A. Math Notes (2005) 78: 563. doi:10.1007/s11006-005-0155-3

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 

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

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