An exponential lower bound for the sum of powers of bounded degree polynomials

摘要

In this work we consider representations of multivariate polynomials in F[x] of the form f(x)=Q1(x)e1+Q2(x)e2++Qs(x)es where the ei's are positive integers and the Qi's are arbitary multivariate polynomials of degree at most d. We give an explicit n-variate polynomial f of degree n such that any representation of the above form for f requires the number of summands s to be 2(nd) .