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Lecture on " Manin's Conjecture for a Class of Singular Hypersurfaces"
DateandTime: 2019-06-13 20:11:42

Speaker:Wu Jie, Professor, Université Paris-Est, France

Date:June 14, 2019

Time: 10:10 am -11:10 am

Location:1032 Lecture Hall, Block B, Zhixin Building, Central Campus

Sponsor:the School of Mathematics

Abstract:

Let $n$ be a positive multiple of $4$ or $n=2$. In this talk, we shall show how to establish an asymptotic formula for the number of rational points of bounded height on singular cubic hypersurfaces $S_n$ defined by $$x^3=(y_1^2 + \cdots + y_n^2)z, $$ by analytic method.

This result is new in two aspects: first, it can be viewed as a modest start on the study of density of rational points on those singular cubic hypersurfaces which are not covered by the classical theorems of Davenport or Heath-Brown; second, it proves Manin's conjecture for singular cubic hypersurfaces $S_n$ defined above.

(Joint works with Regis de la Breteche, Kevin Destagnol, Jianya Liu, Yongqing Zhao)

Bio:

Prof. Wu Jie is a first-class researcher of the National Center for Scientific Research of France and a doctoral supervisor of Université Paris-Est Créteil. He completed his Ph.D from Université Paris-Sud in 1993. In the same year, he joined the National Research Center (CNRS) of France and engaged in the research of number theory. He is an overseas high-level innovative talent introduced by Shandong Province and was awarded the honorary title of Taishan Scholar Overseas Distinguished Expert. His main research interests include many fields such as prime distribution, index sum, module form and L-function. He has published more than 80 papers in international mathematics journals.

For more information, please visit:

http://www.view.sdu.edu.cn/info/1020/119459.htm

Edited by: Wang Yan




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