Let N be sufficiently large odd positive integer. Assume GRH (generalized Riemman hypothesis). It is proved that the equation N=p1+p2+p3,pi-(N/3)≤U,i=1,2,3,U≥N(1/2)log3+ε N has solutions, where pi are primes, and the number of representations has an asymptotic formula.%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-(N/3)≤U, i=1,2,3, U≥N(1/2)logN3+ε有解,此处pi是素数,并得到了方程解数的渐进式.
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