3 problems

Fermat's conjecture over an arithmetic function field. For every arithmetic function field $K$, there exists a positive integer $N_0$ depending on $K$ such that $F_N$ has Fermat's…

Let $F_{N,M}$ be the Fermat curve defined by … and let $F^*_{2,4}$ be the curve $z^2=w^4+1$. Let $\sigma=\sigma_1$, so $\sigma(t)=t^p$. Fermat and related curve conjectures. There…

Generalized Sato–Tate conjecture. The sequence $x_E$ is equidistributed on $\mathcal X_E$ with respect to the image on $\mathcal X_E$ of the Haar measure of $\mathcal G_E$. This pr…