Least zero of pairs of additive cubic equations
Year: 2026
Type: article
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 , see text \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
Source: Forum Mathematicum
Authors: Yixiu Xiao, Hongze Li
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
Award: G7895294006
OpenAlex ID: W4417295476