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Employing Br\"udern's and Wooley's new complification method, we establish anasymptotic Hasse principle for the number of solutions to a system of r_3 cubicand r_2 quadratic diagonal forms, when the number of cubic equations is atleast double the number of quadratic forms. The number of variables required islower than in earlier work. In particular, we achieve essentially square rootcancellation for systems of one quadratic and arbitrarily many cubic equations.

The Hasse principle for systems of quadratic and cubic diagonal equations