## Abstract

Abstract: The class of Dirichlet series associated with a periodic arithmetical function f includes the Riemann zeta-function as well as Dirichlet L-functions to residue class characters. We study the value-distribution of these Dirichlet series L(s; f) and their analytic continuation in the neighbourhood of the critical line (which is the axis of symmetry of the related Riemann-type functional equation). In particular, for a fixed complex number a ≠ 0, we find for an even or odd periodic f the number of a-points of the Δ-factor of the functional equation, prove the existence of the mean of the values of L(s; f) taken at these points, show that the ordinates of these a-points are uniformly distributed modulo one and apply this to show a discrete universality theorem.

Original language | English |
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Pages (from-to) | 238-263 |

Number of pages | 26 |

Journal | Proceedings of the Steklov Institute of Mathematics |

Volume | 314 |

Issue number | 1 |

DOIs | |

Publication status | Published - Sept 2021 |

## Keywords

- critical line
- Dirichlet L-functions
- Dirichlet series
- Julia line
- periodic coefficients
- uniform distribution
- universality

## ASJC Scopus subject areas

- Mathematics (miscellaneous)