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Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
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Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
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eBook
Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
2020
Overview
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 $\\mathbb F_q(t^1/d)$.
Publisher
American Mathematical Society
Subject
ISBN
1470442191, 9781470442194
