Geodesic
On the number of integral polynomialswith bounds placed on the derivative at $p$-adic and real roots
Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 6-10

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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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     author = {M. L. Bezrukov},
     title = {On the number of integral polynomialswith bounds placed on the derivative at $p$-adic and real roots},
     journal = {Trudy Instituta matematiki},
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M. L. Bezrukov. On the number of integral polynomialswith bounds placed on the derivative at $p$-adic and real roots. Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 6-10. http://geodesic.mathdoc.fr/item/TIMB_2017_25_2_a0/