On one proof of the integral representation for the Riemann zeta-function

Vyacheslav I. Kuzovatov

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: This article is devoted to one proof of the integral representation for the Riemann zeta-function. The idea presented in this proof can be useful in studying generalizations of the Riemann zeta-function and constructing integral representations for these generalizations. This integral representation for the Riemann zeta-function is used to obtain a functional relation for it.

Keywords: Riemann zeta-function, integral representation, entire function.

UDC: 517.5

Received: 26.06.2025
Received in revised form: 27.07.2025
Accepted: 28.08.2025

Language: English