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

Essouabri D.; Velásquez Castañón O. · Journal of Number Theory (2020) · DOI: 10.1016/j.jnt.2019.10.026

Resumen

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.

Instituciones: Universidad Nacional de Ingeniería