E-resources
-
Berger, Lisa; Hall, Chris; Pannekoek, Ren e; Park, Jennifer Mun Young; Pries, Rachel; Sharif, Shahed; Silverberg, Alice; Ulmer, Douglas
2020, 2020, 2020-10-30, Volume: 1295eBook
The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\mathbb F_p(t)$, when $p$ is prime and $r\ge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $\mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $\mathbb F_q(t^1/d)$.
