Integral representation of the associated zeta-function and its applications

Abstract: An associated zeta-function constructed from the zeros of an entire function of order less than one is considered. An integral representation for this zeta-function is obtained, providing its analytic continuation. This integral representation is analogous to the integral representation for the classical Riemann zeta-function. As an application of the main result, an explicit integral representation is derived for a zeta-function constructed from the zeros of an entire function of order less than one, where all zeros are real and negative. A specific integral representation for the Riemann zeta-function is obtained as a corollary. It is shown how this representation can be used to derive the functional equation for the Riemann zeta-function.

Russianmathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods