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

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9781470442194

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Author Information

Lisa Berger, Stony Brook University, NY Chris Hall, Western University, London, Ontario, Canada Rene Pannekoek, Imperial College, London, UK Rachel Pries, Colorado State University, Fort Collins, CO Shahed Sharif, California State University San Marcos, CA Alice Silverberg, University of California at Irvine, CA Douglas Ulmer, Georgia Institute of Technology, Atlanta, GA Jennifer Park, University of Michigan, Ann Arbor, MI

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