Polynomial Sums over Automorphs of a Positive Definite Binary Quadratic Form
نویسندگان
چکیده
For each m 3 1, let A(m) = {N E Z x Z : Q(N) = m>. Note that CNEacrn) P(N) = 0 for each m > 1 if and only if e(,; P, Q) = 0. Let G denote the group of integral automorphs (of determinant &l) of Q(X). The first result in [I] states that if P(X) is a spherical polynomial with respect to Q(X) and if O(T; P, Q) E 0, then CUEG P(UX) = 0. The following theorem shows that this result holds for any homogeneous polynomial P(X), spherical or not.
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