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院士论坛、杰出学者讲坛、杰出校友讲坛|
发表时间:2021-03-05 阅读次数:49次
报告题目: 杰出学者讲坛(六十):The BSD Conjecture and Congruent Number Problem
报 告 人:田野 研究员
报告人所在单位:中国科亚投彩票网站app数学与系统科学研究院
报告日期:2021-03-05 星期五
报告时间:10:30:00-11:30
报告地点:光华东主楼2201
  
报告摘要:

A positive integer is called a congruent number if it is the area of some right triangle with rational side-lengths. For example,  5, 6, 7 are congruent numbers since they are area of right triangles with side lengths (3/2, 20/3, 41/6), (3, 4, 5), and (35/12, 24/5, 337/60), respectively. Fermat showed that 1, 2, 3 are not congruent by his famous infinite descent method.  The congruent number problem is to determine whether a given integer is a congruent number.  It has a thousand years of history and has closed relation to the Birch and Swinnerton-Dyer (BSD, for short) conjecture. The BSD conjecture is one of seven millennium problems listed by the Clay Mathematical Institute. It predicts a deep relation between the L-function of an elliptic curve over a number field and its Mordell-Weil group.  The BSD conjecture predicts that any positive integer, congruent to 5, 6, or 7 modulo 8, is a congruent number. In this talk, we will introduce some recent progress on the BSD conjecture and the congruent number problem.

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