Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets

2025/04/10 by Ackelsberg, Ethan, Jamneshan, Asgar · 3 citations
#22F30 #37A15 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 11B13 #Secondary 11B30

paper · doi:10.48550/arxiv.2504.07865

Abstract

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 action of a countable discrete abelian group. We apply this result to establish the existence of triple restricted sumsets in subsets of positive density in arbitrary countable discrete abelian groups, subject to a necessary finiteness condition.

Citations

• Counterexamples to generalizations of the Erdős B+B+t problem
• Problems on infinite sumset configurations in the integers and beyond
• A proof of Erdős's B+B+t conjecture
• The structure of arbitrary Conze-Lesigne systems
• Multiple ergodic averages in abelian groups and Khintchine type recurrence
• Multiple recurrence and large intersections for abelian group actions
• Return times theorem for amenable groups
• Norm convergence of multiple ergodic averages on amenable groups
• Universal characteristic factors and Furstenberg averages
• A Non Conventional Ergodic Theorem for a Nil-System

Cited by

• On density analogs of Hindman's finite sums theorem

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