The Irreducibility of Polynomials Arising from the Study of Fourier Coefficients of Powers of the Dedekind Eta Function

摘要

Heim, Luca and Neuhauser [HLN] introduced a family of polynomials in a variable x related to the n-th Fourier coefficients of powers of the Dedekind eta function. They conjectured among other things that this polynomial sequence contains only irreducible polynomials over ?. We use Newton polygons to establish the irreducibility over ? of these polynomials.