邀请人：陈永高 教授 & 戴丽霞 教授
地点： 行健楼526报告厅
摘要：For any elliptic curve E over 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).
报告人简介：郗平，西安交通大学教授、博士生导师。2004年考入西安交通大学理科试验班，2014年获得博士学位，同年留西安交大任教。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。2020年获得国家杰出青年科学基金，同时主持国家自然科学基金面上项目及中法合作交流项目各一项。