Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions
: Tao, Terence; Teräväinen, Joni
Publisher: European Mathematical Society - EMS - Publishing House GmbH
: BERLIN
: 2025
: Journal of the European Mathematical Society
: Journal of the European Mathematical Society
: J EUR MATH SOC
: 27
: 4
: 1321
: 1384
: 64
: 1435-9855
: 1435-9863
DOI: https://doi.org/10.4171/JEMS/1404(external)
: https://doi.org/10.4171/jems/1404(external)
: https://research.utu.fi/converis/portal/detail/Publication/491829634(external)
We establish quantitative bounds on the U k[N] Gowers norms of the M & ouml;bius function mu and the von Mangoldt function A for all k, with error terms of the shape O((log log N)-c). As a consequence, we obtain quantitative bounds for the number of solutions to any linear system of equations of finite complexity in the primes, with the same shape of error terms. We also obtain the first quantitative bounds on the size of sets containing no k-term arithmetic progressions with shifted prime difference.
:
TT was supported by a Simons Investigator grant, the James and Carol Collins Chair,
the Mathematical Analysis & Application Research Fund Endowment, and by NSF grant DMS1764034. JT was supported by a Titchmarsh Fellowship and funding from the European Union’s Horizon Europe research and innovation programme under Marie Skłodowska-Curie grant agreement no. 10105890
