On a recursive equation over $p$-adic field

TL;DR

This paper provides a complete characterization of solutions to a recursive equation derived from Bethe lattice models within the context of $p$-adic numbers, advancing understanding of $p$-adic recursive structures.

Contribution

It offers a comprehensive description of all solutions to a specific recursive equation related to $p$-adic Bethe lattice models, a novel contribution in this area.

Findings

Complete set of solutions characterized

New insights into $p$-adic recursive equations

Implications for $p$-adic statistical models

Abstract

In the paper we completely describe the set of all solutions of a recursive equation, arising from the Bethe lattice models over $p$-adic numbers.