关于孪生素数猜想与一个配对问题

On Prime Twins Conjecture and a Parity Problem

本文研究 p+h=P_r,p≤x 的解数的阶,所得到的上界恰为人们长期猜测的 c_hxln^(-2)x(lnlnz)^(r-1),而下界与此预料为正确的阶只差一个阶因子 lnlnz.利用这些结果,我们顺便推广和改进了 E.K.S.Ng 与张明尧关于配对问题的工作.

Lower and upper bounds are given to the number of solu- tions of P+h=P_r,P≤x,where x is a sufficiently large positive number,and h(≠0)is a fixed even number.The obtained upper bounds are just the expected results chxln^(-2)x(lnlnx)^(r-1),while the difference between the obtained lower bounds and the expected results is only a order factor lnlnx.Using the lower bounds we get,the work of Eugene K.S.Ng and Zhang Mingyao about the parity problem is generalized and improved.