Hua’s theorem with nine almost equal prime variables

摘要

We sharpen Hua’s result by proving that each sufficiently large odd integer N can be written as $$ N = p_1^3 + cdots + p_9^3 with left| {p_j - sqrt[3]{{N/9}}} right| leqq U = N^{tfrac{1} {3} - tfrac{1} {{198}} + varepsilon } $$ , where p j are primes. This result is as good as what was previously derived from the Generalized Riemann Hypothesis.