Decoupling, exponential sums and the Riemann zeta function

Abstract

We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H]. In particular, this leads to an improved bound $|\zeta (\frac{1}{2}+it)|\ll t^{53/342+\epsilon }$ for the zeta function on the critical line

14 pages

References in corpus (1)

• $l^p$ decouplings for hypersurfaces with nonzero Gaussian curvature

Cited by in corpus (1)

• Asymptotics for cuspidal representations by functoriality from GL(2)