Decoupling, exponential sums and the Riemann zeta function

Abstract

We establish a new decoupling inequality for curves in the spirit of earlier work of C. Demeter and the author which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in the work of Huxley. In particular, this leads to an improved bound | ζ ( 1 2 + i t ) | ≪ t 13 / 84 + ε |\zeta (\frac {1}{2} + it)| \ll t^{13/84 + \varepsilon } for the zeta function on the critical line.