Adam Morgan

Constructing Jacobians of rank 1

Abstract Let 𝐾 be a number field, let g ≥ 1 g\geq 1 be an integer and let f ⁢ ( x ) = ( x − a 1 ) ⁢ ⋯ ⁢ ( x − a 2 ⁢ g + 1 ) ∈ O K ⁢ [ x ] see text f(x)=(x-a_{1})\cdots(x-a_{2g+1})\in O_{K}[x] be a polynomial that splits into 2 ⁢ g + 1 2g+1 distinct linear factors. Write 𝐶 for the...