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Exact upper bounds for the number of the polynomials with given discriminants |
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| Authors: | Vasili Bernik Natalia Budarina Fridrich Götze |
| Institution: | 1.Institute of Mathematics,Minsk,Belarus;2.Dublin Institute of Technology,Dublin,Ireland;3.Institute for Applied Mathematics, Khabarovsk Division,Far-Eastern Branch of the Russian Academy of Sciences,Khabarovsk,Russia;4.Universit?t Bielefeld, Fakult?t für Mathematik,Bielefeld,Germany |
| Abstract: | We generalize the result of Davenport on the sum of absolute values of discriminants of integer polynomials of degree three. For the first time, we find the exact upper bound for the number of polynomials with given discriminant in the class of cubic polynomials of bounded height for the whole interval of values of discriminants. |
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