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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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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


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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Additional Information
  • J. Bourgain
  • Affiliation: Institute for Advanced Study, Princeton, New Jersey 08540
  • MR Author ID: 40280
  • Email:
  • 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:
  • MathSciNet review: 3556291