Arithmetic Study Group: The theta lift in the case of SU(1,1), II
13 December 2011 16:00 in CM219
The theory of theta functions tells us that the representation numbers of positive definite quadratic forms are modular forms. This idea can be extended to quadratic forms of indefinite signature in a coherent way, and this gives rise to the idea of a theta lift. We will define a theta lift in the setting of a complex vector space of signature (1,1), which takes weakly holomorphic modular functions to meromorphic modular forms of weight 2, and briefly explain the construction of the lift. We will also present some results of lifting different modular functions e.g. 1, real analytic Eisenstein series, Klein j-invariant. This follows on from the work of Kudla, Millson, Funke, Bruinier and others.