Pruim, Jefta (2024) Is there a fake function field analogue for the Ankeny-Artin-Chowla Conjecture? Master's Thesis / Essay, Mathematics.
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Abstract
Let D ≡ 1 mod 4 be a prime. Then the Ankeny-Artin-Chowla conjecture claims that for the smallest a, b ∈ N that satisfy a^2 − Db^2 = ±4, we have that D ∤ b. Inspired by a similar notion in the case of number fields, we describe fake real quadratic orders in function fields and use these to formulate an analogue of the Ankeny-Artin-Chowla conjecture. We find that this analogue is false in general. We provide horizontal asymptotics when the constant field is finite, which are largely inspired by unpublished work of Florian Hess, Renate Scheidler and Michael John Jacobson. We also find conditions under which the analogue holds and we observe what happens when changing the fake real quadratic order in natural ways.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Muller, J.S. and Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 10 Oct 2024 10:25 |
| Last Modified: | 11 Oct 2024 08:50 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/34308 |
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