On the Distribution Modulo one of the a-Points of the k th Derivative of an L-Function in the Selberg Class

Let F be an L-function from the Selberg class, F ^(k) be the kth derivative of F and a be an arbitrary fixed complex number. The solutions of F ^(k)(s)= a are called a-points. In this paper, we present a new zone without a-points of F ^(k) and we show that if F has a polynomial Euler product and satisfies the analogue of the Lindelöf hypothesis, then the a-points of F ^(k) are uniformly distributed modulo one.