Möbius disjointness for nilsequences along short intervals

XIAOGUANG HE; ZHIREN WANG

doi:10.1090/tran/8176

Möbius disjointness for nilsequences along short intervals

XIAOGUANG HE, ZHIREN WANG

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

For a nilmanifold G/γ, a 1-Lipschitz continuous function F and the Möbius sequence μ(n), we prove a bound on the decay of the averaged short interval correlation 1 HN Σ n≤N lΣ h≤H μ(n + h)F(gn+hx)l as H,N →∞. The bound is uniform in g ∈ G, x ∈ G/γ and F.

Original language	English (US)
Pages (from-to)	3881-3917
Number of pages	37
Journal	Transactions of the American Mathematical Society
Volume	374
Issue number	6
DOIs	https://doi.org/10.1090/tran/8176
State	Published - 2021

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/tran/8176

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title = "M{\"o}bius disjointness for nilsequences along short intervals",

abstract = "For a nilmanifold G/γ, a 1-Lipschitz continuous function F and the M{\"o}bius sequence μ(n), we prove a bound on the decay of the averaged short interval correlation 1 HN Σ n≤N lΣ h≤H μ(n + h)F(gn+hx)l as H,N →∞. The bound is uniform in g ∈ G, x ∈ G/γ and F.",

author = "XIAOGUANG HE and ZHIREN WANG",

year = "2021",

doi = "10.1090/tran/8176",

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AB - For a nilmanifold G/γ, a 1-Lipschitz continuous function F and the Möbius sequence μ(n), we prove a bound on the decay of the averaged short interval correlation 1 HN Σ n≤N lΣ h≤H μ(n + h)F(gn+hx)l as H,N →∞. The bound is uniform in g ∈ G, x ∈ G/γ and F.

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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ER -

Möbius disjointness for nilsequences along short intervals

Abstract

All Science Journal Classification (ASJC) codes

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