Number theory

In his investigation of modular forms of half-integral weight, Shimura established, using Hecke theory, a family of relations between eigneforms of half-integral weight k+1/2 with a given level 4N and character chi and cusp forms of weight 2k and character chi^2. The level being subsequently determined by Niwa to be at most 2N. Kohnen later defined his plus-space, and showed that their Shimura lift images are of level N. On the other hand, Borcherds constructed a regularized theta lift, which for the appropriate lattice take vector-valued weakly holomorphic modular forms of weight k+1/2 to meromorphic modular forms of weight 2k. We show how to obtain, from a scalar-valued modular form of half-integral weight, a vector-valued modular form whose Borcherds lift becomes its Shimura lift. This allows us to extend the Shimura lift construction to weakly holomorphic modular forms, as well as explains this interesting phenomenon of squaring of the character in the process. This is joint work with Yingkun Li.

Date: 

Thursday, 17 March, 2016 - 12:00 to 13:15

Repeats every week every Thursday until Thu Jun 16 2016 except Thu Apr 14 2016

Location: 

Ross Building, room 63, Jerusalem, Israel