Domain of meromorphy of a class of Bateman-like totient zeta functions
The main result of this paper describes the meromorphic continuation of a class of Bateman-like totient zeta function associated to a special class of arithmetical multiplicative functions, discovering a comb-like form of the region of meromorphic continuation, and verifying the expected natural bou...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | Perú |
| Institución: | Consejo Nacional de Ciencia Tecnología e Innovación |
| Repositorio: | CONCYTEC-Institucional |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.concytec.gob.pe:20.500.12390/2440 |
| Acceso en línea: | https://hdl.handle.net/20.500.12390/2440 https://doi.org/10.1016/j.jnt.2019.10.026 |
| Access Level: | acceso abierto |
| Palabra clave: | Natural boundary Bateman-like totient zeta-functions Distribution of values of arithmetic functions Meromorphic continuation http://purl.org/pe-repo/ocde/ford#2.04.01 |
| Sumario: | The main result of this paper describes the meromorphic continuation of a class of Bateman-like totient zeta function associated to a special class of arithmetical multiplicative functions, discovering a comb-like form of the region of meromorphic continuation, and verifying the expected natural boundary by clustering logarithmic type singularities. Then, a standard application of the Selberg-Delange classical method allows us to derive the distribution of values of a class of multivariate multiplicative functions. We also use Balazard-Diamond convolution method to improve in some cases the error term given by Selberg-Delange classical method. © 2020 Elsevier Inc. |
|---|