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 |ζ( 12+it)| t53/342+ for the zeta function on the critical line
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