Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
Author(s)
Bibliographic Information
Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
（Memoirs of the American Mathematical Society, no. 1295）
American Mathematical Society, c2020
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Note
"July 2020, volume 266, number 1295 (fifth of 6 numbers)"
Includes bibliographical reference (p. 129-131)
Description and Table of Contents
Description
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 $\mathbb F_q(t^1/d)$.
by "Nielsen BookData"