F-signature functions of diagonal hypersurfaces

Alessio Caminata, Samuel Shideler, Kevin Tucker +1

Let $f$ be a diagonal hypersurface in $A_p={\mathbb{F}}_p[[x_1,\dots ,x_n]]$. We study the behavior of the function $ϕ_{f,p}({a}/{p^e})=p^{-ne}\dim_{\mathbb{F}_p}\big(A_p/(x_1^{p^e},\…