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 $\mathbb Q\left(X_0(N)\right)$ using Hilbert's irreducibility theorem and modular forms. We also consider computational aspect of the problem using MAGMA and SAGE.
On the arithmetic of generalized Fekete polynomials
Power residues of Fourier coefficients of modular forms
Computation of Galois groups associated to the 2-class towers of some quadratic fields
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