Plancherel-Rotach Asymptotics for $q$-Laguerre Orthogonal Polynomials with Complex Scaling
| dc.creator | Zhang, Ruiming | |
| dc.date | 2006-12-02 | |
| dc.date.accessioned | 2026-07-07T07:34:36Z | |
| dc.date.available | 2026-07-07T07:34:36Z | |
| dc.description | In this work we study the Plancherel-Rotach type asymptotics for $q$-Laguerre orthogonal polynomials with complex scaling . The main term of the asymptotics contains Ramanujan function $A_{q}(z)$ for the scaling parameter on the vertical line $\Re(s)=2$, while the main term of the asymptotics involves the theta function for the scaling parameter in the strip $0<\Re(s)<2$. In the latter case the number theoretical property of the scaling parameter completely determines the order of the error term. $ $These asymptotic formulas may provide insights to some new random matrix model and add a new link between special functions and number theory. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0612058 | |
| dc.identifier | http://arxiv.org/abs/math/0612058 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119819 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 30E15;33D45 | |
| dc.title | Plancherel-Rotach Asymptotics for $q$-Laguerre Orthogonal Polynomials with Complex Scaling | |
| dc.type | text |