小区间上的三素数定理(英文)

The three primes theorem in short intervals

设N是充分大的奇数,本文在广义Riemman假设下证明了方程N=p1+p2+p3,pi-N3≤U,i=1,2,3,U≥N21(logN)3+ε有解,此处pi是素数,并得到了方程解数的渐进式.

Let N be sufficiently large odd positive integer. Assume GRH （general- ized Riemman hypothesis）. It is proved that the equation N = P1＋P2＋P3,｜ Pi-N/3｜≤U,i=1,2,3,U≥N1/2log^3＋ε N has solutions, where plare primes, and the number of representations has an asymptotic formula.