Towards the Sato–Tate groups of trinomial hyperelliptic curves
نویسندگان
چکیده
We consider the identity component of Sato-Tate group Jacobian curves form $$C_1\colon y^2=x^{2g+2}+c, C_2\colon y^2=x^{2g+1}+cx, C_3\colon y^2=x^{2g+1} +c,$$ where $g$ is genus curve and $c\in\mathbb Q^*$ constant. approach this problem in three ways. First we use a theorem Kani-Rosen to determine splitting Jacobians for $C_1$ 4 5 prove what each case. then higher by finding maps lower computing pullbacks differential 1-forms. In using method, are able relate $C_1$, $C_2$, $C_3$. Finally, develop new method groups families curves. compute many explicit examples, find surprising patterns shapes components these
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2021
ISSN: ['1793-7310', '1793-0421']
DOI: https://doi.org/10.1142/s1793042121500822