报告题目：Lang--Trotter conjecture for CM elliptic curves
报告人： 郗平 教授
报告时间：2021年5月20日（周四）下午16：00-17:00
报告地点：藕舫楼702
主持人： 方金辉 教授
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、Algebra & Number Theory、International Mathematics Research Notices等国际数学期刊。
报告摘要：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).
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数学与统计学院
2021年5月19日
