Work

The Paucity Problem for Certain Symmetric Diophantine Equations

Year: 2022

Type: article

Abstract: Let $\varphi _1,\ldots ,\varphi _r\in {\mathbb Z}[z_1,\ldots z_k]$ be integral linear combinations of elementary symmetric polynomials with $\text {deg}(\varphi _j)=k_j\ (1\le j\le r)$ , where $1\le k_1 . Subject to the condition $k_1+\cdots +k_r\ge \tfrac {1}{2}k(k-~1)+2$ , we show that there is a paucity of nondiagonal solutions to the Diophantine system $\varphi _j({\mathbf x})=\varphi _j({\mathbf y})\ (1\le j\le r)$ .

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s000497272200096x

Author: TREVOR D. WOOLEY

Institution: Purdue University West Lafayette

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,255

Funder: National Science Foundation