Higher uniformity of bounded multiplicative functions in short intervals on average

DOI10.4007/annals.2023.197.2.3OpenAlexW4319066955MaRDI QIDQ2684549

Kaisa Matomäki, Joni Teräväinen, Tamar Ziegler, Maksym Radziwiłł, Terence C. Tao

Publication date: 16 February 2023

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.15644

zbMATH Keywords

nilsequencessign patternsChowla conjectureLiouville functionGowers uniformity

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Arithmetic combinatorics; higher degree uniformity (11B30) Relations between ergodic theory and number theory (37A44)

Related Items

On the Hardy–Littlewood–Chowla conjecture on average, Higher uniformity of arithmetic functions in short intervals I. All intervals, On arithmetic functions orthogonal to deterministic sequences, Chowla and Sarnak conjectures for Kloosterman sums

Cites Work

• Multiplicative functions in short intervals
• The quantitative behaviour of polynomial orbits on nilmanifolds
• The Möbius function is strongly orthogonal to nilsequences
• The primes contain arbitrarily long polynomial progressions
• An averaged form of Chowla's conjecture
• Linear equations in primes
• Sarnak's conjecture: what's new
• The logarithmic Sarnak conjecture for ergodic weights
• Polynomials. Translated from the second Russian edition by Dimitry Leites.
• Fourier uniformity of bounded multiplicative functions in short intervals on average
• On the orbits of multiplicative pairs
• The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
• Higher order Fourier analysis of multiplicative functions and applications
• THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS
• Structure and Geometry of Lie Groups
• An Inequality Arising in Genetical Theory
• Möbius disjointness for nilsequences along short intervals
• Large character sums: Pretentious characters and the Pólya-Vinogradov theorem
• On the representation of large odd integer as a sum of three almost equal primes
• Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures
• Pure and mixed exponential sums
• VINOGRADOV'S INTEGRAL AND BOUNDS FOR THE RIEMANN ZETA FUNCTION
• Sarnak’s conjecture for sequences of almost quadratic word growth
• Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds
• Discorrelation Between Primes in Short Intervals and Polynomial Phases
• Odd order cases of the logarithmically averaged Chowla conjecture
• POLYNOMIAL PATTERNS IN THE PRIMES
• Lie Groups, Lie Algebras, and Representations
• AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
• A Holder Type Inequality for Symmetric Matrices with Nonnegative Entries
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
• An inverse theorem for the Gowers \(U^{s+1}[N\)-norm]
• A new proof of Szemerédi's theorem
• On the Möbius function in all short intervals
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• Unnamed Item
• Unnamed Item
• Unnamed Item