Elliptic curves and L-functions

椭圆曲线和 L 函数

• 批准号: 155635-2008
• 负责人: David, Chantal
• 金额: $ 1.09万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503633
• 关键词: Elliptic; curves; functions

My research interests are mainly elliptic curves and L-functions. In the last years, I studied several distribution problems associated with elliptic curves over the rationals, in collaboration with several co-authors. This is a very active research area, and I intend to extend my previous work in various different directions in the next years. For example, a conjecture of N. Koblitz gives an exact asymptotic for the number of primes such that the group of points modulo p of a given elliptic curve over Q has prime order. This has applications to public key cryptography. In a recent work with A. Balog and A. Cojocaru, we proved that Koblitz's conjecture is true on average, when one takes the average over all elliptic curves in a box. This work raises a lot of new interesting questions, which are addressed in this proposal.

我的研究兴趣主要是椭圆曲线和L-函数。在过去的几年里，我研究了几个分配问题与椭圆曲线的有理数，在合作与几个共同作者。这是一个非常活跃的研究领域，我打算在未来几年内将我以前的工作扩展到各个不同的方向。例如，N. Koblitz给出了一个精确的渐近素数的数量，使一个给定的椭圆曲线上的点群模p有素数阶。这在公钥密码学中有应用。在最近的一项工作中，A。和A. Cojocaru，我们证明了Koblitz猜想平均是正确的，当一个人在一个盒子里的所有椭圆曲线的平均值。这项工作提出了许多新的有趣的问题，这些问题在本提案中得到了解决。