منابع مشابه
Couniformization of Curves over Number Fields
— We study correspondences between projective curves over Q̄.
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Let E be an elliptic curve over Q, with L-function LE(s). For any primitive Dirichlet character χ, let LE(s, χ) be the L-function of E twisted by χ. In this paper, we use random matrix theory to study vanishing of the twisted L-functions LE(s, χ) at the central value s = 1. In particular, random matrix theory predicts that there are infinitely many characters of order 3 and 5 such that LE(1, χ)...
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The main result of this paper is that an elliptic curve having good reduction everywhere over a real quadratic field has a 2-rational point under certain hypotheses (primarily on class numbers of related fields). It extends the earlier case in which no ramification at 2 is allowed. Small fields satisfying the hypotheses are then found, and in four cases the non-existence of such elliptic curves...
متن کاملNumber of Jacobi quartic curves over finite fields
In this paper the number of Fq-isomorphism classes of Jacobi quartic curves, i.e., the number of Jacobi quartic curves with distinct jinvariants, over finite field Fq is enumerated.
متن کاملRanks of Elliptic Curves with Prescribed Torsion over Number Fields
We study the structure of the Mordell–Weil group of elliptic curves over number fields of degree 2, 3, and 4. We show that if T is a group, then either the class of all elliptic curves over quadratic fields with torsion subgroup T is empty, or it contains curves of rank 0 as well as curves of positive rank. We prove a similar but slightly weaker result for cubic and quartic fields. On the other...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2003
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(02)00197-4