Year: 2025
Type: preprint
Abstract: We establish multiple recurrence results for pretentious measure-preserving multiplicative actions along generalized Pythagorean triples, that is, solutions to the equation $ax^2 + b y^2 = c z^2$. This confirms the ergodic-theoretic form of the generalized Pythagorean partition regularity conjecture in this critical case of structured measure-preserving actions. As a consequence of our main theorem, any finite coloring of $\mathbb{N}$ generated by the level sets of finitely many pretentious completely multiplicative functions, must contain a monochromatic generalized Pythagorean triple.
Source: arXiv (Cornell University)
Authors: Frantzikinakis, Nikos, Mountakis, Andreas
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6948038956
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