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.
Granville, Abc allows us to count squarefrees , International Mathematics Research Notices 19 (1998), 991–1009
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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.