On the Distribution Modulo One of the a-Points of the Kth 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 with- out a-points of F (k) and we show that if F has a polynomial Euler product and satisfies the analogue of the Lindelo¨f hypothesis, then the a-points of F (k) are uniformly distributed modulo one.