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math.NT2026
Improved bounds in Birch's theorem for forms in many variables
Yijie Diao, Lena Wurzinger
We improve the best known result on the number of variables needed for the smooth Hasse principle for homogeneous forms of degree \(d\geq5\).
math.NT2026
Average root numbers in two isotrivial families of elliptic curves
Yijie Diao
We study root numbers in the isotrivial families and . For a broad class of fixed binary forms, we prove that the average root number over primitive pairs e…