Document Type
Lecture
Publication Date
9-5-2017
Abstract
The results of Bergelson-Host-Kra and Leibman state that a multiple correlation can be decomposed into sum of a nilsequence (a sequence defined by evaluating a continuous function along an orbit in a nilsystem) and a null sequence (a sequence that tends to zero in density). I refine their results by showing the null sequence tends to zero in density along primes. In this talk, I sketch the proof whose main ingredient is Green-Tao’s theorem on orthogonality between W-tricked von Mangoldt function and nilsequences. I also briefly explain how Tao and Teravainen use above refinement to prove odd cases of logarithmic Chowla conjecture.
Relational Format
presentation
Recommended Citation
Lê, Anh, "Nilsequences and multiple correlations along primes with application to Chowla conjecture" (2017). Algebra/Number Theory Seminar. 31.
https://egrove.olemiss.edu/math_algebra_number_theory/31
