Publicación:
Domain of meromorphy of a class of Bateman-like totient zeta functions
Domain of meromorphy of a class of Bateman-like totient zeta functions
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Fecha
2020
Autores
Essouabri, Driss
Velásquez Castañón, Oswaldo
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Academic Press Inc.
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Abstracto
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.
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Palabras clave
Natural boundary,
Bateman-like totient zeta-functions,
Distribution of values of arithmetic functions,
Meromorphic continuation