ar X iv : m at h / 02 12 34 4 v 1 [ m at h . N T ] 2 6 D ec 2 00 2 AVERAGE NORMS OF POLYNOMIALS

In this paper we study the average L2α-norm over T -polynomials, where α is a positive integer. More precisely, we present an explicit formula for the average L2α-norm over all the polynomials of degree exactly n with coefficients in T , where T is a finite set of complex numbers, α is a positive integer, and n ≥ 0. In particular, we give a complete answer for the cases of Littlewood polynomials and polynomials of a given height. As a consequence, we derive all the previously known results for this kind of problems, as well as many new results.