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 Tr. Inst. Mat., 2017, Volume 25, Number 2, Pages 6–10 (Mi timb273)

On the number of integral polynomialswith bounds placed on the derivative at $p$-adic and real roots

M. L. Bezrukov

Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: Consider a class of polynomials defined by a fixed degree and a fixed height. Introducing an additional constraint on the value of the $p$-adic norm of the derivative at a $p$-adic root, we find an upper bound on the number of such polynomials. A similar bound has been proved in the case where the derivative is bounded at a real and a $p$-adic root.

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UDC: 511.42

Citation: M. L. Bezrukov, “On the number of integral polynomialswith bounds placed on the derivative at $p$-adic and real roots”, Tr. Inst. Mat., 25:2 (2017), 6–10

Citation in format AMSBIB
\Bibitem{Bez17} \by M.~L.~Bezrukov \paper On the number of integral polynomialswith bounds placed on the derivative at $p$-adic and real roots \jour Tr. Inst. Mat. \yr 2017 \vol 25 \issue 2 \pages 6--10 \mathnet{http://mi.mathnet.ru/timb273}