Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields, Paperback / softback Book

Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields Paperback / softback

Part of the Memoirs of the American Mathematical Society series

Paperback / softback

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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 $\mathbb F_q(t^1/d)$.

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