题目：Jacobi forms of weight one on Gamma_0(N) 

报告人：王好武教授 武汉大学

时间：2024年10月20日（周日）上午10:30

地点：东区第五教学楼5107教室

摘要：Jacobi forms are mixtures of modular forms on SL(2,Z) and elliptic functions. Their theory was first proposed by Eichler and Zagier in 1985, and has a wide range of applications in mathematics and theoretical physics. Jacobi forms of low weight are rare and difficult to construct. Let J_{1,m}(N) be the vector space of Jacobi forms of weight one and index m on \Gamma_0(N). In 1985, Skoruppa proved that J_{1,m}(1)=0 for any m. In 2007, Ibukiyama and Skoruppa proved that J_{1,m}(N)=0 for any squarefree N and any m that is coprime to N. In this talk, we extend their results. We determine all levels N separately, such that for any m, J_{1,m}(N)=0; or for any m that is coprime to N, J_{1,m}(N)=0. We also establish explicit dimension formulas of J_{1,m}(N) when m is coprime to N or m is squarefree. This is joint work with my student Jialin Li.