Research Of Singular Series For Goldbach Problems

By the means that D.A.Goldston researched the tail of the singular series G_2y（k）for even Goldbach problem,we research G_ty（k）.And by the means that Montgomery and Soundarar-ajan researched the singular series G₂（k）for even Goldbach problem,we research the singular series G₃（k）for odd Go ldbach problem.At last,we obtain two asymptotic formulas for sum from k≤n （N-k）² G_ty（k）² and sum from k≤n（N-k）G₃（k）.Theorem 1 We have,for1 ≤ y ≤N^1/2and any fixed δ（0<δ<1）,Theorem 2 For N ≥ 1,...