
Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
American Mathematical Society (Publisher)
Will be published approx. on 30. October 2020
Book
Paperback/Softback
131 pages
978-1-4704-4219-4 (ISBN)
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 $\mathbb F_q(t^1/d)$.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
270 gr
ISBN-13
978-1-4704-4219-4 (9781470442194)
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Schweitzer Classification
Persons
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
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