BEHAVIOR OF NONELLIPTIC POLYNOMIALS AT INFINITY

摘要

The paper investigates the behavior of polynomials depending on two variables at infinity. Some necessary and sufficient conditions for ∣P(ζ_1,ζ_2)∣→ ∞ as ∣ζ∣ = ((ζ_1~2)+(ζ_2~2))~(1/2) → ∞ are obtained in terms of multiplicities of zeros of the homogeneous sub-polynomials P_j (j = 0,1,2), P(ζ_1,ζ_2) = P_0(ζ_1,ζ_2) + P_1(ζ_1,ζ_2) + P_2(ζ_1,ζ_2).