Towards the Sato-Tate Groups of Trinomial Hyperelliptic Curves

Melissa Emory, Heidi Goodson, Alexandre Peyrot

We consider the identity component of the Sato-Tate group of the Jacobian of curves of the form $$C_1:y^2=x^{2g+2}+c,C_2:y^2=x^{2g+1}+cx,C_3:y^2=x^{2g+1}+c,$$…