Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero
نویسندگان
چکیده
منابع مشابه
Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero
This paper provides evidence for the Birch and Swinnerton-Dyer conjecture for analytic rank 0 abelian varieties Af that are optimal quotients of J0(N) attached to newforms. We prove theorems about the ratio L(Af , 1)/ΩAf , develop tools for computing with Af , and gather data about certain arithmetic invariants of the nearly 20, 000 abelian varieties Af of level ≤ 2333. Over half of these Af ha...
متن کاملA p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
Mazur, Tate, and Teitelbaum gave a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for elliptic curves. We provide a generalization of their conjecture in the good ordinary case to higher dimensional modular abelian varieties over the rationals by constructing the padic L-function of a modular abelian variety and showing it satisfies the appropriate interpolation property. We descri...
متن کاملVisibility and the Birch and Swinnerton-Dyer conjecture for analytic rank zero
Let E be an optimal elliptic curve over Q of conductor N having analytic rank zero, i.e., such that the L-function LE(s) of E does not vanish at s = 1. Suppose there is another optimal elliptic curve over Q of the same conductor N whose Mordell-Weil rank is greater than zero and whose associated newform is congruent to the newform associated to E modulo a power r of a prime p. The theory of vis...
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1 Algebraic Groups 7 1.1 Group Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Restriction of Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Algebraic Groups over a Nonalgebraically Closed Field K . . . . . . . . . . . 13 1.4 Structure of Algebraic Groups . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Topologizing G(R...
متن کاملThe Birch-swinnerton-dyer Conjecture
We give a brief description of the Birch-Swinnerton-Dyer conjecture which is one of the seven Clay problems.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2004
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-04-01644-8