Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

Learn about DMJ's founding and visit DMJ By the Numbers for key facts about this flagship journal.

  • ISSN: 0012-7094 (print), 1547-7398 (electronic)
  • Publisher: Duke University Press
  • Discipline(s): Mathematics
  • Full text available in Euclid: 1935--
  • Access: By subscription only
  • Euclid URL: https://projecteuclid.org/dmj

Featured bibliometrics

MR Citation Database MCQ (2018): 2.79
JCR (2018) Impact Factor: 2.199
JCR (2018) Five-year Impact Factor: 2.766
JCR (2018) Ranking: 15/313 (Mathematics)
Article Influence (2018): 4.346
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2018): 5.73

Indexed/Abstracted in: Current Contents: Physical, Chemical & Earth Sciences, IBZ Online, Magazines for Libraries, MathSciNet, Science Citation Index, Science Citation Index Expanded, Scopus, and zbMATH

Featured article

The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures

Terence Tao and Joni Teräväinen Volume 168, Number 11 (2019)
Abstract

Let g0,,gk:ND be 1-bounded multiplicative functions, and let h0,,hkZ be shifts. We consider correlation sequences f:NZ of the form f(a):=m1logωmxm/ωmnxmg0(n+ah0)gk(n+ahk)n, where 1ωmxm are numbers going to infinity as m and is a generalized limit functional extending the usual limit functional. We show a structural theorem for these sequences, namely, that these sequences f are the uniform limit of periodic sequences fi. Furthermore, if the multiplicative function g0gk “weakly pretends” to be a Dirichlet character χ, the periodic functions fi can be chosen to be χ-isotypic in the sense that fi(ab)=fi(a)χ(b) whenever b is coprime to the periods of fi and χ, while if g0gk does not weakly pretend to be any Dirichlet character, then f must vanish identically. As a consequence, we obtain several new cases of the logarithmically averaged Elliott conjecture, including the logarithmically averaged Chowla conjecture for odd order correlations. We give a number of applications of these special cases, including the conjectured logarithmic density of all sign patterns of the Liouville function of length up to three and of the Möbius function of length up to four.

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