TY - JOUR

T1 - Riemann-type functional equations

T2 - Julia line and counting formulae

AU - Sourmelidis, Athanasios

AU - Steuding, Jörn

AU - Suriajaya, Ade Irma

N1 - Funding Information:
The first author was supported by Austrian Science Fund , Projects F-5512 and Y-901 and the third author was supported by JSPS KAKENHI Grant Number 18K13400 .
Publisher Copyright:
© 2022 Royal Dutch Mathematical Society (KWG)

PY - 2022/11

Y1 - 2022/11

N2 - 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.

AB - 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.

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U2 - 10.1016/j.indag.2022.08.002

DO - 10.1016/j.indag.2022.08.002

M3 - Article

AN - SCOPUS:85136570469

SN - 0019-3577

VL - 33

SP - 1236

EP - 1262

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 6

ER -