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 ??0<?<1?,Theorem 2 For N ? 1,...