CUSP FORMS AND NUMBER OF REPRESENTATIONS OF POSITIVE INTEGERS BY DIRECT SUM OF BINARY QUADRATIC FORMS

In this study, we calculated all reduced primitive binary quadratic forms which are . We find the theta series\ud , Eisenstein part of\ud and the generalized theta series which are cusp forms by computing some spherical functions of second order with respect to Q . We obtain a basis of the subspace of\ud . Explicit formulas are obtained for the number of representations of positive integers by all direct sum of three quadratic forms\u