"Nice" Rational Functions

2013/12/06 by Allan J. MacLeod, MacLeod, Allan J.
Mathematics · #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1312.1793

openalex publication_date 2013/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider simple rational functions R_mn(x)=P_m(x)/Q_n(x), with P_m and Q_n polynomials of degree m and n respectively. We look for "nice" functions, which we define to be ones where as many as possible of the roots, poles, critical points and (possibly) points of inflexion are integer or, at worst, rational.

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