Counting extensions of imaginary quadratic fields
Alexandr Bene\v{s}
TL;DR
This paper develops an asymptotic formula for counting quadratic extensions with bounded discriminant over quadratic fields with odd class number, extending known results from the rational field.
Contribution
It generalizes existing asymptotic formulas from Q to quadratic fields with odd class number, advancing understanding of quadratic extension distributions.
Findings
Derived an asymptotic count for quadratic extensions over quadratic fields
Extended known results from rational numbers to quadratic fields
Provides new insights into the distribution of quadratic extensions
Abstract
The goal is to obtain an asymptotic formula for the number of quadratic extensions with bounded discriminant of a some quadratic number field with odd class number. This extends an already known result for Q.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Mathematical Dynamics and Fractals