Geodesic
Upper bounds for the number of integer polynomials with given discriminants
Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 29-36

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A generalization of the Gelfond theorem on the smallest value of the two integer polynomials without common roots was obtained, taking into account the evaluation of all their derivatives. 
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     author = {N. V. Budarina and D. Dickinson and V. I. Bernik},
     title = {Upper bounds for the number of integer polynomials with given discriminants},
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N. V. Budarina; D. Dickinson; V. I. Bernik. Upper bounds for the number of integer polynomials with given discriminants. Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 29-36. http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a3/