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Integral Hasse principle for Markoff type cubic surfaces (2408.06846v1)
Published 13 Aug 2024 in math.NT
Abstract: We establish new upper bounds on the number of failures of the integral Hasse principle within the family of Markoff type cubic surfaces $x2+ y2+ z2- xyz= a$ 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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