On Artin's Conjecture: Pairs of Additive Forms

Abstract

It is established that for every pair of additive formsvariables the equations f = g = 0 have a non-trivial p-adic solution for all odd primes. * for 0 ≤ ν ≤ p. Modulo p, each level coefficient vector ãi , bi lies in exactly one of the disjoint sets L ν .