Additive Forms of Different Degrees
by
Michael P. Knapp
University of Michigan

Suppose that f(x) and g(x) are homogeneous additive polynomials with integral coefficients of different degrees k and n, where k > n and k-n is a power of an odd prime. We will establish a bound on the number of variables needed to guarantee that the system f(x)=g(x)=0 has a nontrivial p-adic solution for every prime p.

Date received: March 14, 2000