Rational points on varieties defined by multihomogeneous diagonal forms

Doyon Kim; Tian Wang

doi:10.1016/j.jnt.2026.06.010

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arXiv · 2507.20878

Rational points on varieties defined by multihomogeneous diagonal forms

Doyon Kim·Tian Wang

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Abstract

We give an asymptotic formula for the number of rational points of bounded height on algebraic varieties defined by systems of multihomogeneous diagonal equations. The proof uses the Hardy-Littlewood circle method and the hyperbola method developed by Blomer and Br\"udern.

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Doyon Kim, Tian Wang. 2025-07-28. Rational points on varieties defined by multihomogeneous diagonal forms. https://doi.org/10.1016/j.jnt.2026.06.010

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