Inhomogeneous additive equations.

In this paper, we study the function Δ ∗ (k , n) , which we define as the smallest number s of variables needed to guarantee that the equation ∑ i = 1 s a i x i k + ∑ i = 1 s b i y i n = 0 has nontrivial solutions in each of the p -adic fields ℚ p , regardless of the rational integer coefficients. This generalizes the Γ ∗ (k) function of Davenport and Lewis. In this paper, we give a sharp upper bound for Δ ∗ (k , n) and compute its value for various choices of the degrees. [ABSTRACT FROM AUTHOR]