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In this paper, we propose a new method of upper bounds for the number of integer polynomials of the fourth degree with a given discriminant. By direct calculation similar results were established by H. Davenport and D. Kaliada for polynomials of second and third degrees.
Budarina, Natalia; Bernik, Vasilii; and O'Donnell, Hugh, "New estimates for the number of integer polynomials with given discriminants" (2020). Articles. 89.