9 papers · 1 filter
Quantitative Polynomial Wiener-Wintner Theorems
Lars Becker, Asgar Jamneshan, Christoph Thiele
We prove quantitative polynomial Wiener--Wintner theorems in a very general setup, including measure-preserving actions of nilpotent Lie groups. Our results apply both to ergodic a…
The non-ergodic Host-Kra-Ziegler structure theorem for -actions via measurable selections
Asgar Jamneshan, Simon Machado
We establish a non-ergodic version of the Host-Kra-Ziegler structure theorem for measure-preserving -actions. Our argument reduces the non-ergodic case to the ergodic…
Local rigidity of self-joinings and factors of pro-nilsystems
Pauwel Van Den Eeckhaut, Asgar Jamneshan
It is an immediate consequence of the ergodic structure theorem of Host and Kra that every factor of an ergodic -step pro-nilsystem is again an ergodic -step pro-nilsystem. I…
Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets
Ethan Ackelsberg, Asgar Jamneshan
The aim of this paper is to establish a Ratner-type equidistribution theorem for orbits on homogeneous spaces associated with 2-nilpotent locally compact Polish groups under the ac…
A Host--Kra -system of order that is not Abramov of order , and non-measurability of the inverse theorem for the norm
Asgar Jamneshan, Or Shalom, Terence Tao
It was conjectured by Bergelson, Tao, and Ziegler \cite{btz} that every Host--Kra $\F_p^Ï$-system of order is an Abramov system of order . This conjecture has been verified…
Polynomial towers and inverse Gowers theory for bounded-exponent groups
Asgar Jamneshan, Or Shalom, Terence Tao
In this paper we develop Host--Kra and inverse Gowers theory for abelian groups of bounded exponent. We show that the Host--Kra factors associated with act…