Yossi Moshe, Université Ben Gourion, Beersheva, Israël, et LRI, Orsay

On subword decomposition and balanced polynomials

Let H(x) be a polynomial over Z and p a prime number. For n ≥ 0
and a in {1,..., p-1}, let N_a(n) denote the number of coefficients in
Hⁿ, belonging to the residue class a + pZ. We show that the existence
of certain patterns in the base p representation of n forces N_a(n) and
N_b(n) to be almost equal. Then, using Kingman's subadditive ergodic
theorem, we study the asymptotical behavior of