On Dirichlet approximation polynomials and some properties of Dirichlet $L$-functions

In this paper we study the analytic properties of Dirichlet $L$ -functions in the critical strip, characteristic for almost periodic functions. The research is based on Approximation approach, consisting in the construction of Dirichlet polynomials, which are almost periodic functions, "rapidly convergent" in the critical strip to Dirichlet $L$ -functions.
On this path, for any rectangle lying in the critical strip, the existence of $\varepsilon $ -almost period for the Dirichlet L-function, we obtain the estimate constants of uniform continuity. Issues related to studying other properties of Dirichlet $L$ -functions are discussed.