The number of integer polynomials whose discriminants are divided by a large prime power.

Authors

  • M. A. Kalugina Faculty of Computer Systems and Networks, Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
  • V. I. Bernik Department of Number Theory, Institute of Mathematics of the National Academy of Sciencesof Belarus, Minsk, Belarus

Keywords:

Integer polynomials, the discriminant of a polynomial, estimates from above for the number of polynomials, p-adic norm, prime power

Abstract

The number of integer polynomials whose discriminants are divided by a large prime power.

References

V. Beresnevich, V. Bernik, F. G.otze, The distribution of close conjugate algebraicnumbers, Compos. Math. 146 (2010), no. 5, 1165–1179.

D. Koleda, On an estimate from above of the number of third-degree integer polynomials with a given boundary of discriminants,Vestsi NAS Belarusi. Ser. fiz.-mat. navuk (2010),no. 3, 10–16 (in Russian).

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