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 $\mathbb F_q(t^1/d)$.
ISBN: | 9781470442194 |
Publication date: | 30th October 2020 |
Author: | Lisa Berger, Chris Hall, René Pannekoek, Jennifer Mun Young Park, Rachel Pries, Shahed Sharif, Alice Silverberg, Douglas Ulmer |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 131 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Calculus and mathematical analysis |