Modular forms of degree n and representation by quadratic forms V

Abstract

Let A, B be integral symmetric positive definite matrices of degree m and two, respectively, and suppose that A[X] = B is soluble over Zp for every prime p. If m ≥ 7 and min B = min B[x] (Z2 ∋ x i≠ 0) is sufficiently large, then A[X] = B is soluble over Z. We gave a conditional result for m = 6 in [7] under an assumption on the estimate from above of a kind of generalized Weyl sums. Here we give an unconditional result for special sequences of B.