Necessary and sufficient conditions are given for monogenic number fields arising from roots of polynomials composed as f(x^k + b) for two families of irreducible f, along with asymptotic counts and an application to non-square-free discriminants.
Dedekind, Über den zusammenhang zwischen der theorie der ideale und de r theorie der höheren kongruenzen , Göttingen Abhandlungen 23 (1878), 1–23
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Monogenic Fields from Polynomial Compositions with Applications
Necessary and sufficient conditions are given for monogenic number fields arising from roots of polynomials composed as f(x^k + b) for two families of irreducible f, along with asymptotic counts and an application to non-square-free discriminants.