Integral Hasse principle for Markoff type cubic surfaces

2024/08/13 by Hrishabh Mishra, Mishra, Hrishabh
Mathematics · #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2408.06846

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|≤ A as A→ ∞. 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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