# Moscow Mathematical Journal

Volume 22, Issue 1, January–March 2022  pp. 1–68.

The ∗-Markov Equation for Laurent Polynomials

Authors:  Giordano Cotti (1) and Alexander Varchenko (2)
Author institution:(1) Faculdade de Ciências da Universidade de Lisboa - Grupo de Física Matemática, Campo Grande Edifício C6, 1749-016 Lisboa, Portugal
(2) Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA;
Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Leninskiye Gory 1, 119991 Moscow GSP-1, Russia

Summary:

We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which appears as an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov equation and its solutions are reflected in the properties of the $*$-Markov equation and its solutions.

2020 Math. Subj. Class. 11D25, 14F08, 34M40

Keywords: Markov equation, symmetric Laurent polynomial, trees, Poisson structure.