Abstract:

This paper discusses two problems. Firstly the authors give the Schwarz
formula for a holomorphic function in unit disc when the boundary value of its real part
is in the class H of generalized functions in the sense of Hua. Secondly the authors use
the classical Schwarz formula to give a new proof of the zero free region of the Riemann
zeta-function.

Key words: Schwarz formula;zero free region;Riemann zeta-function