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

Abstract Let F be an L -function from the Selberg class, F ( k ) be the k th 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.