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

Abstract

In this paper we discuss applications of the theory developed in [21] and [22] in studying certain Galois groups and splitting fields of rational functions in Q (X 0 (N )) using Hilbert's irreducibility theorem and modular forms. We also consider computational aspect of the problem using MAGMA and SAGE.2000 Mathematics Subject Classification. 11F11.