English

Decoupling, exponential sums and the Riemann zeta function

Number Theory 2016-02-23 v2

Abstract

We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H]. In particular, this leads to an improved bound ζ(12+it)t53/342+ε|\zeta(\frac 12+it)|\ll t^{53/342+\varepsilon} for the zeta function on the critical line

Keywords

Cite

@article{arxiv.1408.5794,
  title  = {Decoupling, exponential sums and the Riemann zeta function},
  author = {Jean Bourgain},
  journal= {arXiv preprint arXiv:1408.5794},
  year   = {2016}
}

Comments

14 pages

R2 v1 2026-06-22T05:38:48.823Z