On the real projections of zeros of almost periodic functions

Abstract

This paper deals with the set of the real projections of the zeros of an arbitrary almost periodic function defined in a vertical strip $U$. It provides practical results in order to determine whether a real number belongs to the closure of such a set. Its main result shows that, in the case that the Fourier exponents $\{{\lambda }_1,{\lambda }_2,{\lambda }_3,\dots \}$ of an almost periodic function are linearly independent over the rational numbers, such a set has no isolated points in $U$.