A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions
Tekijät: Tao, Terence; Teräväinen, Joni
Kustantaja: European Mathematical Society - EMS - Publishing House GmbH
Kustannuspaikka: BERLIN
Julkaisuvuosi: 2025
Journal: Journal of the European Mathematical Society
Tietokannassa oleva lehden nimi: Journal of the European Mathematical Society
Lehden akronyymi: J EUR MATH SOC
Vuosikerta: 27
Numero: 4
Aloitussivu: 1321
Lopetussivu: 1384
Sivujen määrä: 64
ISSN: 1435-9855
eISSN: 1435-9863
DOI: https://doi.org/10.4171/JEMS/1404
Verkko-osoite: https://doi.org/10.4171/jems/1404
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/491829634
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.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
Julkaisussa olevat rahoitustiedot:
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
