Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function
The Lindelöf-Wirtinger expansion of the Lerch transcendent function implies, as a limiting case, Hurwitz's formula for the eponymous zeta function. A generalized form of Möbius inversion applies to the Lindelöf-Wirtinger expansion and also implies an inversion formula for the Hurwitz zeta function a...
| Autores: | ; ; |
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| Tipo de documento: | Artículo |
| Estado: | Accepted version |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc6987b750603269e81cdc |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc6987b750603269e81cdc |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Fourier series Lerch transcendent function Möbius inversion |
| Sumario: | The Lindelöf-Wirtinger expansion of the Lerch transcendent function implies, as a limiting case, Hurwitz's formula for the eponymous zeta function. A generalized form of Möbius inversion applies to the Lindelöf-Wirtinger expansion and also implies an inversion formula for the Hurwitz zeta function as a limiting case. The inverted formulas involve the dynamical system of rotations of the circle and yield an arithmetical functional equation. |
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