Polynomials in Many Variables: Real vs Complex Norms Original Research Article

We study, for polynomials in many variables, the relations between the complex and the real sup-norms, and we give estimates involving the leading coefficients. We consider the case when the polynomial has a given degree, or some concentration at a given degree. The present paper is a contribution to a general field of investigation: For polynomials in many variables, what are the estimates independent of the number of variables?