Explicit solutions to the Oppenheim conjecture for indefinite ternary diagonal forms

Youssef Lazar

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arXiv · 2101.02076

Explicit solutions to the Oppenheim conjecture for indefinite ternary diagonal forms

Youssef Lazar

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Abstract

We prove the Oppenheim conjecture for indefinite ternary diagonal forms of the type $x^{2}+y^{2} -\alpha z^{2}$ where $ \alpha $ is an irrational number. Our method is explicit in the sense that we are able to construct a solution to the problem and we obtain an effective bound on the solution. The method is geometrical and is based on continued fractions.

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Youssef Lazar. 2021-01-06. Explicit solutions to the Oppenheim conjecture for indefinite ternary diagonal forms. https://arxiv.org/abs/2101.02076

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