Agarwal, Prakhar (2025) On the divisibility of class numbers of quadratic number fields. Bachelor's Thesis, Mathematics.
|
Text
bMATH2025AgarwalP.pdf Download (1MB) | Preview |
|
![[img]](https://fse.studenttheses.ub.rug.nl/style/images/fileicons/text.png) |
Text
Toestemming.pdf Restricted to Registered users only Download (181kB) |
Abstract
In this thesis, we study aspects of the divisibility of the class numbers of quadratic number fields. We prove that there are infinitely many quadratic fields K such that g | h(K) for g ≥ 2. Of special interest is the case g = 2, where we are able to provide an elementary proof, due to Gauss. We also establish quantitative estimates on the density of quadratic number fields K with g | h(K) for g > 2. Finally, we consider the problem of constructing quadratic fields with high p-rank in their class group. We compute explicit examples of imaginary quadratic fields with 5-rank ≥ 3, and prove a lower bound on the p-rank of the class group of a general number field.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Ozman, E. and Kilicer, P. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 17 Jul 2025 11:00 |
| Last Modified: | 17 Jul 2025 11:00 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36349 |
Actions (login required)
 |
View Item |