A Novel Difference-Integral Equation Satisfied Asymptotically by the Riemann Zeta Function

In 2009 Fokas began a program of study of the investigation of the large t-asymptotics of the Riemann zeta function, $$\zeta (\sigma +it)$$ . In the current work we present a novel difference-integral equation which is satisfied asymptotically by $$\zeta (1/2+it)$$ . This equation is obtained starting with a singular integral equation presented for the first time in 2019 and using a finite Fourier transform representation of the Riemann zeta function. The relevant analysis involves a plethora of tools and techniques developed by Fokas and collaborators during the last decade.