Least zero of pairs of additive cubic equations

Abstract An effective upper bound is established for the least non-trivial integer solution to the system of cubic forms (1) { F = c 1 ⁢ x 1 3 + c 2 ⁢ x 2 3 + ⋯ + c n ⁢ x n 3 = 0 , G = d 1 ⁢ x 1 3 + d 2 ⁢ x 2 3 + ⋯ + d n ⁢ x n 3 = 0 , \displaystyle{}\left\{\begin{aligned} \displaystyle{}F&\displaystyle=c_{1}x_{1% }^{3}+c_{2}x_{2}^{3}+\cdots+c_{n}x_{n}^{3}=0,\\ \displaystyle G&\displaystyle=d_{1}x_{1}^{3}+d_{2}x_{2}^{3}+\cdots+d_{n}x_{n}^% {3}=0,\\ \end{aligned}\right. under the “ M -good” condition for n ≥ 16 {n\geq 16} , where c 1 , … , c n {c_{1},\dots,c_{n}} and

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