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 M ¨obius inversion applies to the Lindelöf-Wirtinger expansion and also implies an inversion formula for the Hurwitz zeta function...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de Zaragoza |
| Repositorio: | Zaguán. Repositorio Digital de la Universidad de Zaragoza |
| OAI Identifier: | oai:zaguan.unizar.es:64340 |
| Acceso en línea: | http://zaguan.unizar.es/record/64340 |
| Access Level: | acceso abierto |
| 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 M ¨obius 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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