Congruent Number Problem and Elliptic Curves
Academy of Mathematics and System Science, Chinese Academy of Sciences, Researcher Research interests:Elliptic Curve, Automorphic Form, BSD Conjecture, L-Function, Relative Trace Formula His homepage is http://www.mcm.ac.cn/faculty/tianye/201409/t20140916_255888.html
A positive integer is called a congruent number if it is the area of a right triangle with rational side lengthes. Fibonacci showed that 5, 6, 7 are all congruent and Fermat showed that 1, 2, 3 are not. The congruent number problem is to determine whether a given positive integer is congruent number or not. In this lecture, we give an introduce to this problem and its relation with the Birch and Swinnerton-Dyer conjecture.