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Quartic Polynomials in Two Variables Do Not Represent All Non-negative Integers by Xiao, Stanley Yao; Yamagishi, Shuntaro is a scholarly article available to read on EtoBox.

What is Quartic Polynomials in Two Variables Do Not Represent All Non-negative Integers about?

In this paper, we prove that there does not exist $F \in \mathbb{Q}[x,y]$ of degree $4$ such that $F(\mathbb{Z}^2) = \mathbb{Z}_{\geq 0}$. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials.

Author

Xiao, Stanley Yao; Yamagishi, Shuntaro

Published

2023

Language

EN