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EXPLICIT ROOT NUMBERS OF ABELIAN VARIETIES.
- Source :
-
Transactions of the American Mathematical Society . 12/1/2019, Vol. 372 Issue 11, p7889-7920. 32p. - Publication Year :
- 2019
-
Abstract
- The Birch and Swinnerton-Dyer conjecture predicts that the parity of the algebraic rank of an abelian variety over a global field should be controlled by the expected sign of the functional equation of its L-function, known as the global root number. In this paper, we give explicit formulae for the local root numbers as a product of Jacobi symbols. This enables one to compute the global root number, generalising work of Rohrlich, who studies the case of elliptic curves. We provide similar formulae for the root numbers after twisting the abelian variety by a self-dual Artin representation. As an application, we find a rational genus two hyperelliptic curve with a simple Jacobian whose root number is invariant under quadratic twist. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ABELIAN varieties
*ELLIPTIC curves
*FUNCTIONAL equations
*L-functions
*BIRCH
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 372
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 139656927
- Full Text :
- https://doi.org/10.1090/tran/7926