TY - JOUR
T1 - Riemann-type functional equations
T2 - Julia line and counting formulae
AU - Sourmelidis, Athanasios
AU - Steuding, Jörn
AU - Suriajaya, Ade Irma
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.
KW - a-points
KW - Extended Selberg class
KW - Functional equation
KW - Landau formula
KW - Riemann–von Mangoldt formula
UR - https://doi.org/10.1016/j.indag.2022.08.002
UR - http://www.scopus.com/inward/record.url?scp=85136570469&partnerID=8YFLogxK
U2 - 10.1016/j.indag.2022.08.002
DO - 10.1016/j.indag.2022.08.002
M3 - Article
SN - 0019-3577
VL - 33
SP - 1236
EP - 1262
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 6
ER -