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,... .
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REFERENCES
K. Mahler, “On algebraic differential equations satisfied by automorphic functions,” J. Austral. Math. Soc., 10 (1969), 445–450.
V. V. Zudilin, “Diophantine problems for q-zeta values,” Mat. Zametki [Math. Notes], 72 (2002), no. 6, 936–940.
Yu. V. Nesterenko, Transcendence of Some Functions [in Russian], Manuscript (2003).
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Translated from Matematicheskie Zametki, vol. 78, no. 4, 2005, pp. 608–613.
Original Russian Text Copyright ©2005 by Yu. A. Pupyrev.
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Pupyrev, Y.A. Linear and Algebraic Independence of q-Zeta Values. Math Notes 78, 563–568 (2005). https://doi.org/10.1007/s11006-005-0155-3
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DOI: https://doi.org/10.1007/s11006-005-0155-3