论文标题
某些对称二芬太汀方程的稀疏问题
The paucity problem for certain symmetric Diophantine equations
论文作者
论文摘要
令$φ_1，\ ldots，φ_r\ in \ mathbb z [z_1，\ ldots z_k] $是基本对称多项式的积分线性组合，$ \ text {deg}（deg}（φ_j）（φ_j） <k_r = k $。在情况$ k_1+\ ldots+k_r \ ge \ tfrac {1} {2} {2} k（k-1）+2 $的前提下，我们表明，对Diophantine System $φ_j（\ MATHBF x）= m nate $ j $ j $ j $ j $ j $ j $ j $ j.jj（\ mathbf x）
Let $φ_1,\ldots ,φ_r\in \mathbb Z[z_1,\ldots z_k]$ be integral linear combinations of elementary symmetric polynomials with $\text{deg}(φ_j)=k_j$ $(1\le j\le r)$, where $1\le k_1<k_2<\ldots <k_r=k$. Subject to the condition $k_1+\ldots +k_r\ge \tfrac{1}{2}k(k-1)+2$, we show that there is a paucity of non-diagonal solutions to the Diophantine system $φ_j(\mathbf x)=φ_j(\mathbf y)$ $(1\le j\le r)$.
