On zeros of linear combinations of functions of special form related to the Hecke L-functions of imaginary quadratic fields on short intervals

Abstract

For arithmetic Dirichlet series satisfying a functional equation of Riemann type but admitting no Euler product expansions, lower bounds of the correct order of magnitude for the number of their zeros on intervals of the critical line Re s = 1/2 have not been obtained so far. The first to show that the critical line contains abnormally many zeros of an arithmetic Dirichlet series without Euler products was Voronin, who proved in 1980 [3] that