On the Vertical Distribution of Values of $L$-functions in the Selberg Class

Abstract

We prove explicit formulae for $\alpha$-points of $L$-functions from the Selberg class. Next we extend a theorem of Littlewood on the vertical distribution of zeros of the Riemann zeta-function $\zeta (s)$ to the case of $\alpha$-points of the aforementioned $L$-functions. This result implies the uniform distribution of subsequences of $\alpha$-points and from this a discrete universality theorem in the spirit of Voronin is derived.

28 pages