Domain of meromorphy of a class of Bateman-like totient zeta functions

• Autores: Essouabri, Driss, Velásquez Castañón, Oswaldo
• Formato: artículo
• Fecha de Publicación: 2020
• Institución: Consejo Nacional de Ciencia Tecnología e Innovación
• Repositorio: CONCYTEC-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.concytec.gob.pe:20.500.12390/2440
• Enlace del recurso: https://hdl.handle.net/20.500.12390/2440; https://doi.org/10.1016/j.jnt.2019.10.026
• Nivel de acceso: acceso abierto
• Materia: 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

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.