Yijie Dao

Root number variation on families of elliptic surfaces

We study the elliptic surface families $y^2=x^3+F(z,w)$ and $y^2=x^3+G(z,w)x$ over $\mathbb{Q}$, where $F,G$ are binary forms with integer coefficients. For $100\%$ of forms of any fixed degree ordered by height,
we obtain weak asymptotic formulae for the average root number.