郗平- Lang-Trotter conjecture for CM elliptic curves

点击:    日期:2021-04-14

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 mathematicaeCompositio MathematicaInternational Mathematics Research NoticesMathematische Zeitschrift等国际数学期刊。。

 

时间:2021415星期四 15:00-16:00

地点腾讯会议,会议ID296 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

 

 



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