Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem
In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., [...] N=p13+…+pj3 with [...] |pi−(N/j)1/3|≤N1/3−δ+ε(1≤i≤j), for some [...] 0<δ≤190. Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.