On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function

Abstract: In this paper we study the distribution of zeros of each entire function of the sequence , which approaches the Riemann zeta function for , and is closely related to the solutions of the functional equations . We determine the density of the zeros of on the critical strip where they are situated by using almost-periodic functions techniques. Furthermore, by using a theorem of Kronecker, we also establish a formula for the number of zeros of inside certain rectangles in the critical strip. [Copyright &y& Elsevier]