讲座内容：

Tunnell's formula states that the quadratic n-twisted L-value of the congruent number elliptic curve is proportioanl to the square of the n-th Fourier coefficient of a weight 3/2 modular form, and it has striking applications to the classical congruent number problem. In this talk, I will first review Tunnell's formula and explain how it connects with Waldspurger's fundamental results on Fourier coefficients of half integral weight modular forms, then discuss a generalization (joint with Wei He and Ye Tian).