In the last section , we prove minor arcs integral / has a smaller upper bound 在最后一节，证明劣弧的积分有一个较小的上界。
2.
The weighted number of solutions of equation , r ( b ) , is expressed as the sum of a integral on [ 0 , 1 ] and a remainder term . using the circle method , the integral on the interval [ 0 , 1 ] is divided into the integrals on major arcs and minor arcs respectively , j and j . the section 3 gives a transformation for sj ( a ) and simplifies / 把三次方程的加权解个数r ( b )表示为[ 0 , 1 ]上的积分加上余项，然后利用圆法，把区间[ 0 , 1 )上的积分变成优弧和劣弧的积分和第三节，给出s _ i ( )的一个变换，并化简把的主项被分成m _ 1 ， m _ 2和m _ 3
