Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields (eBook)

Lisa A Berger (Autor)

eBook Download: PDF

131 Seiten
American Mathematical Society (Verlag)
978-1-4704-6253-6 (ISBN)

Infos

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

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 1-4704-6253-2 / 1470462532
• ISBN-13: 978-1-4704-6253-6 / 9781470462536