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Decoupling, exponential sums and the Riemann zeta function
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Journal Article
Decoupling, exponential sums and the Riemann zeta function
2017
Overview
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(12+it)|≪t13/84+ε|\\zeta (\\frac {1}{2} + it)| \\ll t^{13/84 + \\varepsilon } for the zeta function on the critical line.
Publisher
American Mathematical Society
Subject
