Aplicacion de la descomposicion racional univariada a monstrous moonshine (in Spanish)

TL;DR

This paper applies computational algebra techniques, specifically univariate rational function decomposition, to analyze replicable functions in Monstrous Moonshine, identifying all rational relations with integer coefficients between pairs of these functions.

Contribution

It introduces a novel application of rational function decomposition to study modular functions related to Monstrous Moonshine, computing all integer coefficient rational relations between pairs of replicable functions.

Findings

Computed all rational relations with integer coefficients between pairs of replicable functions.

Demonstrated the effectiveness of algebraic techniques in analyzing modular functions.

Enhanced understanding of the structure of replicable functions in Monstrous Moonshine.

Abstract

This paper shows how to use Computational Algebra techniques, namely the decomposition of rational functions in one variable, to explore a certain set of modular functions, called replicable functions, that arise in Monstrous Moonshine. In particular, we have computed all the rational relations with coefficients in Z between pairs of replicable functions. ----- En este articulo mostramos como usar tecnicas de Algebra Computacional, concretamente la descomposcion de funciones racionales univariadas, para estudiar un cierto conjunto de funciones modulares, llamadas funciones replicables, que aparecen en Monstrous Moonshine. En concreto, hemos calculado todas las relaciones racionales con coeficientes en Z entre pares de funciones replicables.