2024/12/30 by Noy Soffer Aranov, Aranov, Noy Soffer · 1 citation
Computer Science · Mathematics · #11J04 #11J13 #11J61 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2501.00171
openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the minimal denominator problem in function fields. In particular, we compute the probability distribution function of the the random variable which returns the degree of the smallest denominator Q, for which the ball of a fixed radius around a point contains a rational function of the form (P)/(Q). Moreover, we discuss the distribution of the random variable which returns the denominator of minimal degree, as well as higher dimensional and P-adic generalizations. This can be viewed as a function field generalization of a paper by Chen and Haynes.