Yi-Jie Diao

activity

20212026

most citedDensity of the union of positive diagonal binary quadratic forms

1 citations · 1 across the 5 of their papers we have counts for

collaborators

6 papers

math.NT2026

Prime points on smooth hypersurfaces

Yijie Diao, Shuntaro Yamagishi

Let $F \in Z [x_{1}, \dots, x_{n}]$ be a homogeneous form of degree $d \geq 4$ which defines a smooth hypersurface in $P_{C}^{n - 1}$ . For $n \geq 24 d^{4} 2^{d}$ ,…

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 $y^{2} = x^{3} + a$ and $y^{2} = x^{3} + a x$ . 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 $d$ binary forms ordered by height, with probability $1$ . 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 $t^{2} - d u^{2} = 1$ in a bounded region. We give a lower bound on the size of fundamental sol…

math.NT2021★ 1 cited

Density of the union of positive diagonal binary quadratic forms

Yijie Diao

Let $X$ be a sufficiently large positive integer. We prove that one may choose a subset $S$ of primes with cardinality $O (lo g X)$ , such that a positive proportion of integers less…