Vinogradovās mean value theorem via efficient congruencing, II
Vinogradovās mean value theorem via efficient congruencing, II
We apply the efficient congruencing method to estimate Vinogradov's integral for moments of order 2s, with 1ā©½sā©½k2ā1. Thereby, we show that quasi-diagonal behavior holds when s=o(k2), and we obtain near-optimal estimates for 1ā©½sā©½14k2+k and optimal estimates for sā©¾k2ā1. In this way we come halfway to proving the main conjecture in ā¦