Escape of Mass of the $p$-Cantor Sequence

Noy Soffer Aranov; Steven Robertson

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arXiv · 2510.19417

Escape of Mass of the $p$-Cantor Sequence

Noy Soffer Aranov·Steven Robertson

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Abstract

Let $p$ be a prime. In 2017, Kemarsky, Paulin, and Shapira (KPS) conjectured that any Laurent series over $\mathbb{F}_p$ exhibits full escape of mass with respect to any irreducible polynomial $P(t)\in\mathbb{F}_p[t]$. In 2025, this was shown to be false in the case $p=2$ and $P(t)=t$ by Nesharim, Shapira and the first named author. This work shows that for any odd prime $p$ and any irreducible polynomial $P(t)\in\mathbb{F}_p[t]$, the so-called $p$-Cantor sequence provides a counterexample to the aforementioned conjecture over $\mathbb{F}_p$. Furthermore, the concepts of maximal escape of mass and generic escape of mass are introduced. These lead to two natural variations of the KPS conjecture, both of which are shown to hold for all previous counterexamples.

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Noy Soffer Aranov, Steven Robertson. 2025-10-22. Escape of Mass of the $p$-Cantor Sequence. https://arxiv.org/abs/2510.19417

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