4 papers
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…
math.NT2025
Liouville function, von Mangoldt function and norm forms at random binary forms
Yijie Diao
We analyze the average behavior of various arithmetic functions at the values of degree binary forms ordered by height, with probability . This approach yields averaged vers…
math.NT2024
Class numbers and integer points on some Pellian surfaces
Yijie Diao
We provide an estimate for the number of nontrivial integer points on the Pellian surface in a bounded region. We give a lower bound on the size of fundamental sol…