The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures

DOI10.2140/ant.2019.13.2103zbMath1476.11127arXiv1809.02518OpenAlexW2890529019WikidataQ122911620 ScholiaQ122911620MaRDI QIDQ2278139

Joni Teräväinen, Terence C. Tao

Publication date: 9 December 2019

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.02518

zbMATH Keywords

Chowla's conjecture1-bounded multiplicative functionElliott's conjecture

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Relations between ergodic theory and number theory (37A44)

Related Items

On Furstenberg systems of aperiodic multiplicative functions of Matomäki, Radziwiłł, and Tao, Three conjectures on \(P^+(n)\) and \(P^+(n+1)\) hold under the Elliott-Halberstam conjecture for friable integers, On the Hardy–Littlewood–Chowla conjecture on average, On consecutive values of random completely multiplicative functions, Analytic number theory. Abstracts from the workshop held November 6--12, 2022, Chowla and Sarnak conjectures for Kloosterman sums, Correlation of multiplicative functions over Fq[x$\mathbb {F}_q[x]$: A pretentious approach], Expansion, divisibility and parity: an explanation, Correlations of multiplicative functions along deterministic and independent sequences, The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures, Averaged forms of two conjectures of Erdős and Pomerance, and their applications, Rigidity in dynamics and M

Cites Work

• Multiplicative functions in short intervals
• Multiplicative functions in arithmetic progressions
• An averaged form of Chowla's conjecture
• On \(\varepsilon\)-representations
• Sarnak's conjecture implies the Chowla conjecture along a subsequence
• The logarithmic Sarnak conjecture for ergodic weights
• Rigidity theorems for multiplicative functions
• The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
• THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS
• ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS
• Furstenberg Systems of Bounded Multiplicative Functions and Applications
• Prime Twins and Siegel Zeros
• On the correlation of multiplicative and the sum of additive arithmetic functions
• Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures
• Bounded Cohomology of Discrete Groups
• Nilsequences and multiple correlations along subsequences
• Nilsequences, null-sequences, and multiple correlation sequences
• Odd order cases of the logarithmically averaged Chowla conjecture
• Das asymptotische Verhalten von Summen über multiplikative Funktionen. II
• SIGN PATTERNS OF THE LIOUVILLE AND MÖBIUS FUNCTIONS
• Unnamed Item
• Unnamed Item
• Unnamed Item