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).

熊玮,现为湖南大学数学学院副教授。2004 年在四川大学获得学士学位，2010年在中国科学院获得博士学位。随后在清华大学及新加坡国立大学做博士后。主要研究方向为 Theta 提升及其应用。研究成果发表在 J. Number Theory, Math. Z., Science China Math., Pacific J. Math. 等著名期刊。