Correlations of multiplicative functions and applications

DOI10.1112/S0010437X17007163zbMath1434.11202arXiv1603.08453OpenAlexW3098823914MaRDI QIDQ4978615

Oleksiy Klurman

Publication date: 25 August 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.08453

zbMATH Keywords

correlationmultiplicative functionsDelange's theorem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Goldbach-type theorems; other additive questions involving primes (11P32) Estimates on character sums (11L40)

Related Items (19)

Exponential sums with multiplicative coefficients and applications ⋮ ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS ⋮ On Furstenberg systems of aperiodic multiplicative functions of Matomäki, Radziwiłł, and Tao ⋮ The Erdős discrepancy problem over the squarefree and cubefree integers ⋮ Correlations of multiplicative functions in function fields ⋮ Tao’s resolution of the Erdős discrepancy problem ⋮ Correlation of multiplicative functions over Fq[x$\mathbb {F}_q[x]$: A pretentious approach] ⋮ A note on multiplicative automatic sequences, II ⋮ THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS ⋮ Multiplicative functions that are close to their mean ⋮ The twin prime conjecture ⋮ Rigidity theorems for multiplicative functions ⋮ Good weights for the Erd\H{o}s discrepancy problem ⋮ Fourier uniformity of bounded multiplicative functions in short intervals on average ⋮ On the orbits of multiplicative pairs ⋮ A note on multiplicative functions resembling the Möbius function ⋮ The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures ⋮ Complex valued multiplicative functions with bounded partial sums ⋮ Additive functions in short intervals, gaps and a conjecture of Erdős

Cites Work

• Multiplicative functions in short intervals
• Some unsolved problems
• An averaged form of Chowla's conjecture
• On the regularity of arithmetic multiplicative functions. I, II
• Multiplicative functions with regularity properties. VI
• On a conjecture of Kátai for additive functions
• Additive functions at consecutive integers
• On the distribution function of additive functions
• Multiplicative functions with difference tending to zero
• The Erdős discrepancy problem
• THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS
• Large character sums: Pretentious characters and the Pólya-Vinogradov theorem
• An Erdos-Wintner Theorem for Differences of Additive Functions
• Multiplicative functions at consecutive integers. II
• SIEVING AND THE ERDŐS–KAC THEOREM
• On the distribution of additive arithmetic functions
• On a problem of P. Erdős
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