... linear forms from the preamble to Lemma 6, and extend these conventions in the natural way soas to apply to the set {Λ1, ,Λs}. By the hypotheses of the statement ofTheorem 2, one finds that for ... derive an upper THE HASSE PRINCIPLE FOR PAIRS OF DIAGONAL CUBIC FORMS877bound of the shape (4.5), subject to the constraints (4.4), wherein either the parameter rtis reduced, or else the parameter ... from the consequence (2.3) ofTheorem 3, and on making use of the corresponding symmetrical bounds for J1and J2, the conclusion of Theorem 4 is immediate from (4.2).In preparation for the...