Higher uniformity of arithmetic functions in short intervals I. All intervals

DOI10.1017/fmp.2023.28arXiv2204.03754OpenAlexW4387787910WikidataQ126176050 ScholiaQ126176050MaRDI QIDQ6084156

Xuancheng Shao, Joni Teräväinen, Terence C. Tao, Kaisa Matomäki

Publication date: 31 October 2023

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.03754

zbMATH Keywords

correlationtotal variationarithmetic progressionlarge sievedivisor functionshort intervalvon Mangoldt functionLipschitz functionFourier decompositionnilsequenceDirichlet polynomialSiegel-Walfisz theoremMobius functionHeath-Brown's identityVinogradov lemmadiscorrelation estimatefiltered nilmanifoldquantitative Leibman theoremsmoothness normuniformity estimateuniformity norm

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Arithmetic combinatorics; higher degree uniformity (11B30)

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