# On the equivalence of the scalar and vector equilibrium problems for a pair of functions forming a Nikishin system

## TL;DR

This paper demonstrates that the vector and scalar equilibrium problems are equivalent in the context of the limit zero distribution of Hermite-Padé polynomials for Nikishin systems, unifying two approaches in approximation theory.

## Contribution

It establishes the equivalence between vector and scalar equilibrium problems for Nikishin systems, clarifying their relationship in approximation theory.

## Key findings

- Proves the equivalence of equilibrium problems for Nikishin systems.
- Provides a unified framework for analyzing Hermite-Padé polynomial zeros.
- Enhances understanding of asymptotic zero distribution in approximation theory.

## Abstract

We prove the equivalence of the vector and scalar equilibrium problems which arise naturally in the study of the limit zeros distribution of type I Hermite--Pad\'e polynomials for a pair of functions forming a Nikishin system.