# Riemann-type functional equations: Julia line and counting formulae

Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya

## 抄録

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.

本文言語 英語 Indagationes Mathematicae https://doi.org/10.1016/j.indag.2022.08.002 印刷中 - 2022

• 数学 (全般)

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