## 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.

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.

Original language | English |
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Journal | Israel Journal of Mathematics |

Publication status | Accepted/In press - 6 Jun 2023 |