Distribution of orders in number fields
Nathan Kaplan, Jake Marcinek, and Ramin Takloo-Bighash
TL;DR
This paper investigates how orders are distributed within number fields, providing an asymptotic count for orders with bounded discriminants specifically in quintic fields, advancing understanding of algebraic number theory.
Contribution
It offers a new asymptotic formula for counting orders in the ring of integers of quintic number fields, a novel result in the distribution of algebraic structures.
Findings
Derived an asymptotic formula for orders in quintic fields
Quantified the distribution of orders with bounded discriminants
Enhanced understanding of algebraic number field structures
Abstract
In this paper we study the distribution of orders of bounded discriminants in number fields. We give an asymptotic formula for the number of orders contained in the ring of integers of a quintic number field.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry