Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields (Memoirs of the American Mathematical Society)

About the Author Lisa Berger, Stony Brook University, NYChris Hall, Western University, London, Ontario, CanadaRene Pannekoek, Imperial College, London, UKRachel Pries, Colorado State University, Fort Collins, COShahed Sharif, California State University San Marcos, CAAlice Silverberg, University of California at Irvine, CADouglas Ulmer, Georgia Institute of Technology, Atlanta, GAJennifer Park, University of Michigan, Ann Arbor, MI Product 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 $\mathbb F_q(t^1/d)$.