论文标题
猜想：$ \ mathbb {q} $的椭圆表面的100％具有等级零
Conjecture: 100% of elliptic surfaces over $\mathbb{Q}$ have rank zero
论文作者
论文摘要
基于出现在Nagao，Rosen和Silverman的工作中的椭圆表面等级的等式，我们猜想，当通过其Weierstrass方程的系数大小时，100％的椭圆表面的排名为$ 0 $，并提出了这种概述的术语，并呈现了这种较低的术语。然后，我们讨论如何从对某些$ l $ functions的理解或对表面的本地行为的理解。最后，我们对有限领域的椭圆表面等级做出了猜想，并强调了一些支持它的实验证据。
Based on an equation for the rank of an elliptic surface over $\mathbb{Q}$ which appears in the work of Nagao, Rosen, and Silverman, we conjecture that 100% of elliptic surfaces have rank $0$ when ordered by the size of the coefficients of their Weierstrass equations, and present a probabilistic heuristic to justify this conjecture. We then discuss how it would follow from either understanding of certain $L$-functions, or from understanding of the local behaviour of the surfaces. Finally, we make a conjecture about ranks of elliptic surfaces over finite fields, and highlight some experimental evidence supporting it.
