Since the modularity of elliptic curves over real quadratic was proved, one may ask whether it is possible to replace \\({\\mathbb {Q}}\\) with a real quadratic field K . Following Thorne's idea, we give some assumptions first and prove the modularity of elliptic curves over the \\(...
As an application of Turán sieve, we give upper bounds for the number of elliptic curves defined over Q (T) in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan's conjecture (Cowan in Conjecture: 100% of elliptic surfa...
Construction of Rational Points on Elliptic Curves over Finite Fields We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the curve. For this, we reduce the problem to the task of ...
In this paper, we consider this problem over number fields. We will prove that the existence of a uniform upper bound for the ranks of elliptic curves in this family is equivalent to the convergence of a certain infinite series. This result extends the work of Rubin and Silverberg over ....
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and stacks) important in the study of moduli spaces of curves ...
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The author constructs elliptic curves over the field (-3) with torsion group /3×/3 and ranks equal to 7 and an elliptic curve over the same field with torsion group /3×/6 and rank equal to 6. This is an improvement of results of F. P. Rabarison [Acta Arith. 144, No. 1, 17...
Summary: [For the entire collection see Zbl 0756.00008.] For public key cryptosystems multiplication on elliptic curves can be used instead of exponentiati... T Beth,F Schaefer - Springer-Verlag 被引量: 58发表: 1991年 On the modularity of supersingular elliptic curves over certain totally real ...
Elliptic curvesL-functionsrandom matrix theoryLet E be an elliptic curve over Q with L-function LE(S). We use the random matrix model of Katz and Sarnak to develop a heuristic for the frequency of vanishing of the twisted Lfunctions LE(l, X), as X runs over the Dirichlet characters of...
花了大概5分钟翻了翻,与Knapp的Elliptic Curves对比如下: Knapp写Elliptic Curves,是在简单介绍Elliptic Curves的算术性质的前提下,仔细介绍了Elliptic Curves over \C,由此引出Modular Forms for SL(2,\Z) and Hecke Congruence subgroups;进而在最后两章介绍了描述两... (展开) 10 0回应 > 更多书评 1篇 ...