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arXiv · 2601.06915

Infinite sumsets in $U^k(\Phi)$-uniform sets

Tristán Radić
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Abstract

Extending recent developments of Kra, Moreira, Richter and Roberson, we study infinite sumset patterns in $U^k(\Phi)$-uniform subsets of the integers, defined via the local uniformity seminorms introduced by Host and Kra. We relate the degree $k$ of a $U^k(\Phi)$-uniform set to the existence of a rich variety of sumset patterns. As a counterpart, we stablish higher order parity obstruction to sumsets arising from nilsystems. We also provide examples of $U^k(\Phi)$-uniform sets for applications, including sets arising from the Thue-Morse and Rudin-Shapiro sequences.

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Tristán Radić. 2026-01-11. Infinite sumsets in $U^k(\Phi)$-uniform sets. https://arxiv.org/abs/2601.06915

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