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

Berger, Lisa; Hall, Chris; Pannekoek, Rene; Pries, Rachel; Sharif, Shahed

Softcover

ISBN 10: 1470442191 ISBN 13: 9781470442194

Publisher: American Mathematical Society, 2020

Synopsis

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

About this title

About the Author

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

Edition details

• Publisher: American Mathematical Society
• Publication date: 2020
• Language: English
• ISBN 10: 1470442191
• ISBN 13: 9781470442194
• Binding: Paperback
• Number of pages: 131