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: | ; ; |
|---|---|
| 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 |
| _version_ | 1878732168093499392 |
|---|---|
| author | Navas, L.M. [0000-0002-5742-8679] |
| author2 | Ruiz, F.J. Varona, J.L. [0000-0002-2023-9946] |
| author2_role | author author |
| author_browse | Navas, L.M. [0000-0002-5742-8679] Ruiz, F.J. Varona, J.L. [0000-0002-2023-9946] |
| author_facet | Navas, L.M. [0000-0002-5742-8679] Ruiz, F.J. Varona, J.L. [0000-0002-2023-9946] |
| author_role | author |
| collection | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_3dddeae4d02c1a33fe53a6b1daa7dffd |
| institution | Universidad de La Rioja (UR) |
| instname_str | Universidad de La Rioja (UR) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:portal.dialnet.es:doc/5bbc6987b750603269e81cdc |
| publishDate | 2015 |
| publishDateSort | 2015 |
| reponame_str | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| spelling | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function Navas, L.M. [0000-0002-5742-8679] Ruiz, F.J. Varona, J.L. [0000-0002-2023-9946] Fourier series Lerch transcendent function Möbius inversion 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. https://investigacion.unirioja.es/documentos/5bbc6987b750603269e81cdc |
| spellingShingle | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function Navas, L.M. [0000-0002-5742-8679] Fourier series Lerch transcendent function Möbius inversion |
| status_str | acceptedVersion |
| title | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function |
| title_full | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function |
| title_fullStr | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function |
| title_full_unstemmed | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function |
| title_short | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function |
| title_sort | Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function |
| topic | Fourier series Lerch transcendent function Möbius inversion |
| topic_facet | Fourier series Lerch transcendent function Möbius inversion |
| url | https://investigacion.unirioja.es/documentos/5bbc6987b750603269e81cdc |