We present a probabilistic Las Vegas algorithm for solving sufficiently generic square
polynomial systems over finite fields. We achieve a nearly quadratic running time in the …

We use recent results about linking the number of zeros on algebraic varieties over ℂ,
defined by polynomials with integer coefficients, and on their reductions modulo sufficiently …

We prove a uniform version of the Dynamical Mordell–Lang Conjecture for étale maps; also,
we obtain a gap result for the growth rate of heights of points in an orbit along an arbitrary …

For positive integers and, we introduce and study the notion of-multiplicative dependence
over the algebraic closure of a finite prime field, as well as-linear dependence of points on …

We present lower bounds for the orbit length of reduction modulo primes of parametric
polynomial dynamical systems defined over the integers, under a suitable hypothesis on its …

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We show, under some natural restrictions, that orbits of polynomials cannot contain too
many elements of small multiplicative order modulo a large prime p. We also show that for …

We describe and analyze a randomized algorithm which solves a polynomial system over
the rationals defined by a reduced regular sequence outside a given hypersurface. We show …

We use a result of P. Habegger to show that for all but finitely many integer pairs $(a,
b)\in\mathbb {Z}^ 2$ with $4 a^ 3+ 27b^ 2\ne 0$ at least one of the points\begin …

Let q be a power of the prime number p, let K= F q (t), and let r⩾ 2 be an integer. For points
a, b∈ K which are F q-linearly independent, we show that there exist positive constants N 0 …