Average norms of polynomials

2002/12/26 by Mansour, T.
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0212344

Abstract

In this paper we study the average \NL_2α-norm over T-polynomials, where α is a positive integer. More precisely, we present an explicit formula for the average \NL_2α-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.

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