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Sharp upper bounds for fractional moments of the Riemann zeta function

Number Theory 2019-01-25 v1

Abstract

We establish sharp upper bounds for the 2k2kth moment of the Riemann zeta function on the critical line, for all real 0k20 \leqslant k \leqslant 2. This improves on earlier work of Ramachandra, Heath-Brown and Bettin-Chandee-Radziwi\l\l

Keywords

Cite

@article{arxiv.1901.08423,
  title  = {Sharp upper bounds for fractional moments of the Riemann zeta function},
  author = {Winston Heap and Maksym Radziwiłł and Kannan Soundararajan},
  journal= {arXiv preprint arXiv:1901.08423},
  year   = {2019}
}

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10 pages