| Popis: |
In this work we consider Dirichlet polynomials that belong to the extended Selberg class. Functions in the extend Selberg class satisfy a functional equation similar to the one that the Riemann zeta function satisfies. Thus, for a function from this class it is possible to formulate a statement equivalent to the Riemann's hypothesis. We show that a Dirchlet polynomial from the extend Selberg class satisfies Riemann's hypothesis if and only if its derivative does not have zeros left of the critical line. This result also holds for the Riemann zeta function. Additionally, we give sufficient conditions for the coeficients of a Dirichlet polynomial under which the polynomial satisfies Riemann's hypothesis. |
