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...

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Detalles Bibliográficos
Autores: Essouabri, Driss, Velásquez Castañón, Oswaldo
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
Descripción
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.