New estimates for the number of integer polynomials with given discriminants

Natalia Budarina; Vasilii Bernik; Hugh O’Donnell

doi:10.1007/s10986-019-09455-8

New estimates for the number of integer polynomials with given discriminants

Natalia Budarina, Vasilii Bernik, Hugh O’Donnell

School of Business Technology, Retail and Supply Chain

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Lithuanian Mathematical Journal
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/s10986-019-09455-8 https://doi.org/10.1007/s10986-019-09455-8
Publication status	Published - 1 Jan 2020

Keywords

Diophantine approximation
discriminant of polynomials

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title = "New estimates for the number of integer polynomials with given discriminants",

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AB - 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.

KW - Diophantine approximation

KW - discriminant of polynomials

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New estimates for the number of integer polynomials with given discriminants

Abstract

Keywords

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