Uniform boundedness conjecture for Waring's problem over diagonal forms
Let k∈Nk\in\mathbb{N}k∈N. For each positive integer-valued function C:N→NC:\mathbb{N}\rightarrow\mathbb{N}C:N→N, let PC(k)=supl≥2{SC(k,l)}P_C(k)=\sup_{l\geq 2}\{S_C(k,l)\}PC(k)=supl≥2{SC(k,l)}, where SC(k,l)S_C(k,l)SC(k,l) is the minimum number…