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Improved bounds in Birch's theorem for forms in many variables

Yijie Diao, Lena Wurzinger

Source record

Source: arXiv

Published: Sep 1, 2026

arXiv: 2609.00757

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Source abstract

We improve the best known result on the number of variables needed for the smooth Hasse principle for homogeneous forms of degree d5d\geq5.

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Improved bounds in Birch's theorem for forms in many variables — Mathematical Frontier Network