On the horizontal distribution of zeros of linear combinations of Euler products (Q1876844)

\textit{E. Bombieri} and the author [Duke Math. J. 80, 821--862 (1995; Zbl 0853.11074)] studied the zeros of functions which are linear combinations of Dirichlet series satisfying Riemann's hypothesis and some other conditions such as the existence of an Euler product and the validity of a functional equation. In view of this work, there are reasons to conjecture that almost all zeros of the functions in question lie on the critical line. In the present paper, the author announces (without details of the proofs) density results on zeros lying close to the critical line.