Prime rational functions over a field
Eva Goedhart, Omar Kihel, and Jesse Larone
TL;DR
This paper establishes criteria based on the order of vanishing at infinity and the resultant to determine when a polynomial or rational function over a field is prime.
Contribution
It introduces new sufficient conditions for primality of polynomials and rational functions over fields, utilizing order of vanishing and resultants.
Findings
Provides criteria for primality based on order of vanishing at infinity.
Uses the resultant to characterize prime rational functions.
Offers a theoretical framework for primality testing in algebraic function fields.
Abstract
The aim of this paper is to provide sufficient conditions for when a polynomial or rational function over a field K is prime using its order of vanishing at infinity and the resultant.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions · Advanced Topics in Algebra