Merilä, Ville:
q-Hypergeometric Functions and Irrationality Measures
Bollettino dell'Unione Matematica Italiana Serie 9 3 (2010), fasc. n.1, p. 137-148, (English)
pdf (279 Kb), djvu (99 Kb). | MR 2605916 | Zbl 1208.11085
Sunto
We present a q-analogue of the Rhin-Viola method for the analysis of $\Phi$-adic valuations of the q-gamma factors occurring in the basic Euler-Pochhammer integral representation of the Heine series $2\phi_{1}$. Moreover, we show that this approach yields the best known irrationality measures for $\log_{q}(z)$, $\log_{q}(2)$ and $\zeta_{q}(1)$.
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Zbl 0904.11020
Con il contributo del Ministero per i Beni e le Attività Culturali