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arXiv · 2011.10692

Riemann-Type Functional Equations -- Julia Line and Counting Formulae --

Athanasios Sourmelidis·Jörn Steuding·Ade Irma Suriajaya
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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 $a\neq0$ and a function from the Selberg class $\mathcal{L}$, we prove a Riemann-von Mangoldt formula for the number of a-points of the $\Delta$-factor of the functional equation of $\mathcal{L}$ 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 $\mathcal{L}(s)$ taken at these points.

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Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya. 2020-11-21. Riemann-Type Functional Equations -- Julia Line and Counting Formulae --. https://doi.org/10.1016/j.indag.2022.08.002

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