Annals of Mathematics· 2012Q1
The Möbius function is strongly orthogonal to nilsequences
- 209citations
- Q1SCImago
- 2012year
Short summary
The Möbius function is shown to be strongly asymptotically orthogonal to polynomial nilsequences, a significant result in additive combinatorics.
AI-generated from the title and abstract; the full text is not read.
Key points
- The Möbius function (n) is proven to be strongly asymptotically orthogonal to polynomial nilsequences.
- The nilsequences are defined using polynomial sequences g: Z -> G within a simply-connected nilpotent Lie group G.
- This result connects number theory with the theory of dynamical systems and additive combinatorics.
- The proof relies on advanced techniques from ergodic theory and additive combinatorics.
AI-generated from the title and abstract; the full text is not read.
Abstract
We show that the Mbius function (n) is strongly asymptotically orthogonal to any polynomial nilsequence (F (g(n))) nN . Here, G is a simply-connected nilpotent Lie group with a discrete and cocompact subgroup (so G/ is a nilmanifold ), g : Z G is a polynomial sequence, and
The authors' abstract, as published at the source. Annals of Mathematics, 2012 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics