2025/10/22 by Noy Soffer Aranov, Aranov, Noy Soffer, Steven Robertson +1
Mathematics · #11J61 #11J70 #37P20 #68R15 #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2510.19417
openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Let p be a prime. In 2017, Kemarsky, Paulin, and Shapira (KPS) conjectured that any Laurent series over \mathbbFp exhibits full escape of mass with respect to any irreducible polynomial P(t)∈\mathbbFp[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)∈\mathbbFp[t], the so-called p-Cantor sequence provides a counterexample to the aforementioned conjecture over \mathbbFp. 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.