On the Image Conjecture
Arno van den Essen, David Wright, and Wenhua Zhao
TL;DR
This paper explores the Image Conjecture, its implications for the Vanishing and Jacobian Conjectures, and introduces the Factorial Conjecture, proving several cases of these interconnected mathematical conjectures.
Contribution
It proves various cases of the Image Conjecture and introduces the Factorial Conjecture, establishing new links between these conjectures and the Jacobian Conjecture.
Findings
Proved several cases of the Image Conjecture
Established implications between the Image and Vanishing Conjectures
Proved various cases of the Factorial Conjecture
Abstract
The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of the Image Conjecture and show how it leads to another fascinating and elusive assertion that we here dub the Factorial Conjecture. Various cases of the Factorial Conjecture are proved.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons · Polynomial and algebraic computation