Introduction to the theory of Jacobi modular forms

Doctorants/Post-Doctorants

Lieu: 
Salle séminaire M3-324
Orateur: 
Haowu Wang
Affiliation: 
Université Lille 1
Dates: 
Mercredi, 14 Juin, 2017 - 17:00 - 18:00
Résumé: 

Jacobi forms are holomorphic functions in two complexe variables. They are modular in one variable and abelian (or double periodic) in another variable. The theory was first systematically studied by Eichler and Zagier in 1985. Jacobi forms are an elegant intermediary  among different types of modular forms and have a large number of applications in number theory, algebraic and differential geometry, mathematical and theoretical physics, Lie algebras, etc.

In this talk, we will introduce the definitions and basic properties of Jacobi forms. We will also set forth many explicit  methods to construct Jacobi forms. And  then we will present the structure theorem of Jacobi forms. At the end, as an application we will give new formulas for the number of representations of integers as sums of eight polygonal numbers.