Geodesic
Decoupling, exponential sums and the Riemann zeta function
Bourgain, J.1
1Institute for Advanced Study, Princeton, New Jersey 08540
Journal of the American Mathematical Society, Tome 30 (2017) no. 1, pp. 205-224
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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.
DOI : 10.1090/jams/860

Bourgain, J.  1

1 Institute for Advanced Study, Princeton, New Jersey 08540 
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Bourgain, J. Decoupling, exponential sums and the Riemann zeta function. Journal of the American Mathematical Society, Tome 30 (2017) no. 1, pp. 205-224. doi: 10.1090/jams/860

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