In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degree growth of these iterations. We use these estimates to bound exponentialâ€¦ (More)

Article history: Received 5 March 2010 Revised 25 May 2010 Available online 1 June 2010 Communicated by Arne Winterhof MSC: primary 11K45 secondary 11T23, 37A45, 37F10

In this paper we study the period of vector sequences generated by triangular polynomial systems and we characterize the case when their orbits are of maximal period. Moreover, we estimateâ€¦ (More)

We consider exponential sums with x-coordinates of points qG and qâˆ’1G where G is a point of order T on an elliptic curve modulo a prime p and q runs through all primes up to N (with gcd(q, T )= 1 inâ€¦ (More)

We recall that a polynomial f(X) âˆˆ K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f(X) âˆˆ Z[X] are stable over Q.â€¦ (More)

We estimate multiplicative character sums over the integers with a fixed sum of binary digits and apply these results to study the distribution of products of such integers in residues modulo a primeâ€¦ (More)