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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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LOWER BOUND OF THE NUMBER OF INTEGRAL POLYNOMIALS OF A GIVEN DEGREE WITH A SMALL VALUE OF THE DERIVATIVE AT THE ROOT

Abstract

In the article we obtain a lower bound of the number of integral polynomials of arbitrary degree and bounded height with small values of the derivative at any root of the polynomial.

About the Author

A. S. Kudin
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus


References

1. Спринджук В. Г. Проблема Малера в метрической теории чисел. Минск, 1967.

2. Bernik VI. // Acta Arith. 1983. Vol 42, no 3. P. 219-253.

3. Beresnevich V., Bernik V., Gotze F. // Compos. Math. 2010. Vol 146, no 5. P. 1165-1179.


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ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)