几乎相等的三次华林-哥德巴赫问题的例外集

Exceptional set for sums of almost equal prime cubes

本文证明了对5≤s≤8,几乎所有的满足某些同余条件的正整数N都可以表示为N=p31+···+p3s,|pi-(N/s)1/3|≤N1/3-θs,其中θ5=7261-2ε,θ6=5159-ε,θ7=11333-ε,θ8=19561-ε.

We prove that almost all integers N satisfying some necessary congruence conditions can be written as sum of the form N = p31/31＋ · · · ＋ p3 swith ｜pi-（N/s）｜≤N1/3-θs, where θs =7261- 2ε,5159- ε,11333- ε,19561- εfor s = 5, 6, 7, 8, respectively.