The Minimal Denominator in Function Fields

Abstract: Meiss and Sanders proposed an experiment in which they fix $\delta>0$ and study the statistics of the minimal denominator $Q$ for which there exists a rational $\frac{P}{Q}\in (x-\delta,x+\delta)$, where $x$ is varied. In this talk, I will discuss the history of this problem and its generalizations, as well as the function field analogue of the minimal denominator problem and open questions. This is based off the preprint arxiv.org/pdf/2501.00171.

number theoryrepresentation theory

Audience: researchers in the topic

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University of Utah Representation Theory / Number Theory Seminar