## Decoupling, exponential sums and the Riemann zeta function

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- by J. Bourgain PDF
- J. Amer. Math. Soc.
**30**(2017), 205-224 Request permission

## 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.## References

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## Additional Information

**J. Bourgain**- Affiliation: Institute for Advanced Study, Princeton, New Jersey 08540
- MR Author ID: 40280
- Email: bourgain@math.ias.edu
- Received by editor(s): September 12, 2014
- Received by editor(s) in revised form: October 4, 2015, November 5, 2015, December 31, 2015, and February 19, 2016
- Published electronically: March 17, 2016
- Additional Notes: The author was partially supported by NSF grant DMS-1301619
- © Copyright 2016 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**30**(2017), 205-224 - MSC (2010): Primary 11M06, 11L07
- DOI: https://doi.org/10.1090/jams/860
- MathSciNet review: 3556291