Hilbert's Irreducibility, Modular Forms, and Computation of Certain Galois Groups

2021/06/09 by Iva Kodrnja, Kodrnja, Iva, Goran Muić +1
Computer Science · Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2106.05213

openalex publication_date 2021/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss applications of our earlier work in studying certain Galois groups and splitting fields of rational functions in \mathbb Q(X₀(N)) using Hilbert's irreducibility theorem and modular forms. We also consider computational aspect of the problem using MAGMA and SAGE.

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