Riemann-type functional equations: Julia line and counting formulae

Athanasios Sourmelidis*, Jörn Steuding, Ade Irma Suriajaya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, for a fixed complex number a≠0 and a function from the Selberg class L, we prove a Riemann–von Mangoldt formula for the number of a-points of the Δ-factor of the functional equation of L and an analog of Landau's formula over these points. From the last formula we derive that the ordinates of these a-points are uniformly distributed modulo one. Lastly, we show the existence of the mean-value of the values of L(s) taken at these points.

Original languageEnglish
JournalIndagationes Mathematicae
Early online dateAug 2022
DOIs
Publication statusE-pub ahead of print - Aug 2022

Keywords

  • a-points
  • Extended Selberg class
  • Functional equation
  • Landau formula
  • Riemann–von Mangoldt formula

ASJC Scopus subject areas

  • Mathematics(all)

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