Integral Hasse principle for Markoff type cubic surfaces

Hrishabh Mishra

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arXiv · 2408.06846

Integral Hasse principle for Markoff type cubic surfaces

Hrishabh Mishra

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Abstract

We establish new upper bounds on the number of failures of the integral Hasse principle within the family of Markoff type cubic surfaces $x^2+ y^2+ z^2- xyz= a$ with $|a|\leq A$ as $A\to \infty$. Our bound improves upon existing work of Ghosh and Sarnak. As a result, we demonstrate that the integral Hasse principle holds for a density $1$ of surfaces in certain sparse sequences.

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Hrishabh Mishra. 2024-08-13. Integral Hasse principle for Markoff type cubic surfaces. https://arxiv.org/abs/2408.06846

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