On the non-quadraticity of values of the q-exponential function and related q-series
| dc.creator | Krattenthaler, Christian | |
| dc.creator | Rochev, Igor | |
| dc.creator | Vaananen, Keijo | |
| dc.creator | Zudilin, Wadim | |
| dc.date | 2008-12-15 | |
| dc.date.accessioned | 2026-07-07T12:45:52Z | |
| dc.date.available | 2026-07-07T12:45:52Z | |
| dc.description | We investigate arithmetic properties of values of the entire function $$ F(z)=F_q(z;λ)=\sum_{n=0}^\infty\frac{z^n}{\prod_{j=1}^n(q^j-λ)}, \qquad |q|>1, \quad λ\notin q^{\mathbb Z_{>0}}, $$ that includes as special cases the Tschakaloff function ($λ=0$) and the $q$-exponential function ($λ=1$). In particular, we prove the non-quadraticity of the numbers $F_q(α;λ)$ for integral $q$, rational $λ$ and $α\notin-λq^{\mathbb Z_{>0}}$, $α\ne0$. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0812.2921 | |
| dc.identifier | http://arxiv.org/abs/0812.2921 | |
| dc.identifier | Acta Arith. 136 (2009), no. 3, 243--269 | |
| dc.identifier | doi:10.4064/aa136-3-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221194 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 11J72, 11J82 (Primary); 11C20, 15A15, 33D15 (Secondary) | |
| dc.title | On the non-quadraticity of values of the q-exponential function and related q-series | |
| dc.type | text |