Convergence Abscissas for Dirichlet Series with Multiplicative Coefficients

Ole Fredrik Brevig; Winston Heap

doi:10.1016/j.exmath.2015.10.005

Convergence Abscissas for Dirichlet Series with Multiplicative Coefficients

Number Theory 2018-07-24 v2 Complex Variables

Authors: Ole Fredrik Brevig , Winston Heap

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Abstract

This note deals with the relationship between the abscissas of simple, uniform and absolute convergence for the Dirichlet series $f(s) = \sum_{n=1}^\infty a_n n^{-s}$ , when the coefficients $a_n$ are either multiplicative or completely multiplicative.

Keywords

exponential sums multiplicative functions divisor function

Cite

@article{arxiv.1506.04546,
  title  = {Convergence Abscissas for Dirichlet Series with Multiplicative Coefficients},
  author = {Ole Fredrik Brevig and Winston Heap},
  journal= {arXiv preprint arXiv:1506.04546},
  year   = {2018}
}

Comments

Minor revision. Two new references added. This note has been accepted for publication in Expositiones Mathematicae

Convergence Abscissas for Dirichlet Series with Multiplicative Coefficients

Abstract

Keywords

Cite

Comments

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