Decoupling, exponential sums and the Riemann zeta function

Bourgain, J.

doi:10.1090/jams/860

Decoupling, exponential sums and the Riemann zeta function
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by J. Bourgain

J. Amer. Math. Soc. 30 (2017), 205-224

DOI: https://doi.org/10.1090/jams/860

Published electronically: March 17, 2016

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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 $|\zeta (\frac {1}{2} + it)| \ll t^{13/84 + \varepsilon }$ for the zeta function on the critical line.

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