Products of Many-Variable Polynomials: Pairs That Are Maximal in Bombieri′s Norm

AbstractWe continue the research initiated in Beauzamy et al. (J. Number Theory36 (1990), 219-245) and Beauzamy et al. (to appear) about products of many-variable polynomials. We investigate the pairs (P, Q) which are maximal for products in Bombieri′s norm (that is for which [PQ] is a large as possible) and prove a stability result: if the product [PQ] is close to maximal, then both P and Q are close to extremal polynomials