UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2022-07-01 16:33

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Conference: Bucharest University Faculty of Physics 2019 Meeting


Section: Theoretical Physics and Applied Mathematics


Title:
Bounds for polynomial divisors


Authors:
Doru STEFANESCU


Affiliation:
University of Bucharest, Faculty of Physics


E-mail
doru.stefanescu@gmail.com


Keywords:


Abstract:
We obtain new bounds for the divisors of integer polynomials, deduced from an inequality on Bombieri's l2 weighted norm. We also obtain limits for the smallest divisor of an integer polynomial. In particular such bounds are useful for algorithms of factorization of integer polynomials. We consider P is a nonconstant polynomial in Z[X] and we suppose that Q is a nontrivial divisor of P over Z. In many problems it is important to have a priori information on Q. For example in polynomial factorization a key step is the determination of an upper bound for the coefficients of such a polynomial Q in function of the coefficients and the degree finding. We derive upper bounds for the coefficients of a divisor in function of the weighted l2 norm of E. Bombieri. In particular we obtain bounds for the heights which improving an inequality of B. Beauzamy.