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Levine, Alex 
ORCID: https://orcid.org/0000-0001-9633-9313
(2025)
Quadratic Diophantine equations, the Heisenberg group and formal languages.
Israel Journal of Mathematics, 269 (1).
pp. 337-383.
ISSN 0021-2172
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Abstract
We express the solutions to quadratic equations with two variables in the ring of integers using EDT0L languages. We use this to show that EDT0L languages can be used to describe the solutions to one-variable equations in the Heisenberg group. This is done by reducing the question of solving a one-variable equation in the Heisenberg group to solving an equation in the ring of integers, exploiting the strong link between the ring of integers and nilpotent groups.
| Item Type: | Article |
|---|---|
| Additional Information: | Publisher Copyright: © The Hebrew University of Jerusalem 2025. |
| Uncontrolled Keywords: | quadratic diophantine equations,equations in groups,edt0l languages,nilpotent groups,general mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2600 |
| Faculty \ School: | Faculty of Science > School of Engineering, Mathematics and Physics |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 19 Aug 2026 10:52 |
| Last Modified: | 23 Aug 2026 05:27 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/104234 |
| DOI: | 10.1007/s11856-025-2746-x |
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