Decoupling, exponential sums and the Riemann zeta function

Bourgain, J.¹

¹ Institute for Advanced Study, Princeton, New Jersey 08540

Journal of the American Mathematical Society, Tome 30 (2017) no. 1, pp. 205-224

Résumé

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.

Détail

DOI : 10.1090/jams/860

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