On the correlation of multiplicative and the sum of additive arithmetic functions

DOI10.1090/memo/0538zbMath0824.11056OpenAlexW2000207987MaRDI QIDQ4318176

Peter D. T. A. Elliott

Publication date: 15 November 1995

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0538

zbMATH Keywords

central limit theoremsdistribution functionsslowly oscillating functionsTurán-Kubilius inequalityErdős-Wintner theoremweak convergence to a distribution functionBombieri-Vinogradov theoremscorrelation of multiplicative functionsasymptotic behaviour of sums over multiplicative functionscomplex-valued multiplicative functions of modulus \(\leq 1\)dual of arithmetic operatorsmethod of the stable dualvalue distribution of additive functions on distinct arithmetic progressions

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Arithmetic functions in probabilistic number theory (11K65)

Related Items (19)

ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS ⋮ On Furstenberg systems of aperiodic multiplicative functions of Matomäki, Radziwiłł, and Tao ⋮ Spectral properties of the Möbius function and a random Möbius model ⋮ Twin primes and the parity problem ⋮ Unnamed Item ⋮ The mean values of multiplicative functions. II ⋮ Discrete uniform distribution for a sum of additive functions ⋮ HARMONIC ANALYSIS ON THE POSITIVE RATIONALS. DETERMINATION OF THE GROUP GENERATED BY THE RATIOS ⋮ Ergodicity of the Liouville system implies the Chowla conjecture ⋮ Asymptotics for multilinear averages of multiplicative functions ⋮ Variants of equidistribution in arithmetic progression and the twin prime conjecture ⋮ The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures ⋮ Poisson distribution for a sum of additive functions ⋮ Combinatorial identities and Titchmarsh's divisor problem for multiplicative functions ⋮ Discrete uniform limit law for a sum of additive functions on shifted primes ⋮ VALUE PATTERNS OF MULTIPLICATIVE FUNCTIONS AND RELATED SEQUENCES ⋮ The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures ⋮ Finite and infinite pseudorandom binary words ⋮ Jonas Kubilius and probabilistic number theory some personal reflections

This page was built for publication: On the correlation of multiplicative and the sum of additive arithmetic functions