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arXiv · 2504.07865

Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets

Ethan Ackelsberg·Asgar Jamneshan
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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.

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Ethan Ackelsberg, Asgar Jamneshan. 2025-04-10. Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets. https://arxiv.org/abs/2504.07865

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