Pintz János: Density theorems for the Riemann Zeta-function near to the line Res=1

Abstract:
We prove a series of density theorems for Riemann's zeta-function for the number of zeros lying near to the boundary line Re s =1 of the critical strip.  In particular,  we improve the constant appearing in the exponent of the Halász-Turán density theorem. The proof uses the relatively recent strong estimate for the zeta-function near the line Re s =1 showed by Heath-Brown. The necessary exponential sums were estimated by Heath-Brown via the new results of Wooley and of Bourgain, Demeter and Guth on the Vinogradov's mean value integral.

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