论文标题
Verteilung der Primzahlen和Asymptotikbezüglichder Kongruenzen der Rationalen punkte auf eliptischenkurvenübereinem einem einem endlichenkörper
Verteilung der Primzahlen und Asymptotik bezüglich der Kongruenzen der rationalen Punkte auf elliptischen Kurven über einem endlichen Körper
论文作者
论文摘要
这项工作有两个主要目的。一方面，我们在这项工作中调查了H. esnault在H. eSnault和C. Xu的一致性公式中的一个问题，该问题涉及在当地田地上弹射平面的奇异模型的封闭纤维上的理性点的数量。从渐近分析的角度来看，这个问题对N. Koblitz的问题非常熟悉，而Koblitz的问题又在密码学中具有一些有意义的应用。我们不会试图在这项工作中解决这些问题，而是专注于研究具有非常基本的功能技术的渐近行为。另一方面，我们将有关生成功能的讨论扩展到了全球情况，全球情况是从Riemann Zeta函数和椭圆曲线的$ L $功能中继承了混合性。最后，我们将研究一个模块化表单的示例，在该示例中，我们能够证明一个分析结果，这与Riemann $ξ$功能的Pólya的结果相似。
This work has two main purposes. On the one side we investigate in this work a question of H. Esnault on congruence formula in a construction of H. Esnault and C. Xu for the number of rational points on the closed fiber of a singular model of the projective plane over a local field. From the viewpoint of asymptotic analysis, the question is quite familiar with a question of N. Koblitz, which in turn has some meaningful applications in cryptography. We don't try to solve those questions in this work, but rather concentrate on studying asymptotic behaviours with very elementary techniques of generating functions. On the other side we extend the discussion on generating functions to the global situation, which inherit hybrid-properties from the Riemann zeta function and the $L$-function of elliptic curves. At the end we will look at an example of modular forms, where we are able to prove an analytic result, which is similar to a result of Pólya for the Riemann $ξ$-function.
