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arXiv · 1307.3983

The asymptotic number of integral cubic polynomials with bounded heights and discriminants

D. Kaliada·F. Götze·O. Kukso
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Abstract

In the paper we partially solved the problem of the distribution of the discriminants of integral polynomials in the cubic case. We proved the asymptotic formula for the number of integral cubic polynomials having bounded height and bounded discriminant. The main term of the obtained formula is the best possible for the considered range of polynomial discriminant values.

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D. Kaliada, F. Götze, O. Kukso. 2013-07-15. The asymptotic number of integral cubic polynomials with bounded heights and discriminants. https://doi.org/10.1007/s10986-014-9234-z

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