题目: Lang-Trotter conjecture for CM elliptic curves
摘要: For any elliptic curve $E$ over $\mathbf{Q}$ and any non-zero integer $r$, the Lang-Trotter conjecture has predicted the asymptotic behaviours of the number of good primes $p\leqslant x$, denoted by $\pi_{E,r}(x)$, such that the Frobenius trace of $E$ at $p$ is equal to the given integer $r$. Quite recently, we are able to prove an estimate for $\pi_{E,r}(x)$ which confirms the upper bound part of the conjecture for CM elliptic curves. Moreover, intimate connections of this conjecture and Hardy-Littlewood conjecture can also be established to characterize the shape of the Lang-Trotter constant in $\pi_{E,r}(x)$. This is based on the joint work with Daqing Wan (in progress).
报告人：郗平 （西安交通大学）
报告人简介：郗平，西安交通大学教授，博士生导师，国家杰出青年基金获得者。主要研究领域为数论，涉及代数迹函数的解析理论、素数分布、筛法及自守形式等方面的研究。研究成果发表于Inventiones mathematicae、Compositio Mathematica、International Mathematics Research Notices、Mathematische Zeitschrift等国际数学期刊。。
时间：2021年4月15日，星期四 15:00-16:00
地点：腾讯会议，会议ID：296 101 721
邀请人：吕广世、蒋玉蛟
主办：山东大学澳国立联合理学院
潘承洞数学研究所
山东大学数学学院
