On the distribution of the \(a\)-points of a Selberg class \(L\)-function modulo one (Q2346311)

Let \(F(s)=\sum_{n=1}^{+\infty}\frac{a(n)}{n^s}\), \(s=\sigma+it\), be the Dirichlet series defined in the half-plane \(\sigma>1\). The Selberg class \(\mathcal{S}\) consists of the functions \(F(s)\) satisfying following properties: the Ramanujan hypothesis for the coefficients \(a(n)\), existence the Euler product representation over prime numbers, analytic continuation and certain functional equation. In the paper, the distribution of the \(a\)-points of the \(L\)-functions \(F(s)\) from the class \(\mathcal S\) is considered. It is shown that if \(F\) has a polynomials Euler product and satisfies an analogue of the Lindelöf hypothesis, then the ordinates of the roots of equation \(F(s)=a\) (\(a\) is an arbitrary fixed complex number) are uniformly distributed modulo one. The obtained results extend a similar results for the Riemann zeta function \(\zeta(s)\) gave by \textit{J. Steuding} [in: Analytic and probabilistic methods in number theory. Proceedings of the 5th international conference in honour of J. Kubilius, Lithuania, 2011. Vilnius: TEV. 243--249 (2012; Zbl 1365.11098)].