Yijie Diao

activity

20242026

collaborators

3 papers

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…