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... ally about accurately estimating the upper bound of the number of rational points for a given type of algebraic curves, especially high-dimensional ones, which is closely related to the Diophantine equation.

Finding the number of rational points, and then studying the distribution of these rational points.

In essence, the geometric structure of high-dimensional algebraic varieties tends to be more complex, with more intricate singularities, topological properties, and different h ...

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