Density theorems for Riemann’s zeta-function near the line ${\rm Re}\,s = 1$
Tom 208 / 2023
Streszczenie
We prove a series of density theorems for Riemann’s zeta-function for the number of zeros lying near the boundary line ${\rm Re}\,s = 1$ 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 ${\rm Re}\,s = 1$ 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 Vinogradov’s mean value integral.