## 2009 Number Theory Seminar - 12

- Date: 04/02/2009

University of British Columbia

On computing a basis for the space of half integer weight modular forms

I will give an expository talk about half integer weight modular forms.

Definitions and basic properties of this space will be given. Then, the

Shimura correspondence will be discussed. Roughly speaking, this

associates to a modular form of half integer weight some modular form

of integer weight. This will be followed by a discussion of several

improvements on this result, the most important of which is due to

Waldspurger. In his work Waldspurger used representation theory to

establish an explicit relation between the square of the coefficients

in the q-expansion of a form f of half integer weight k/2 and the

central values of 'twist' L-series for a form g of integer weight k-1

corresponding to f via the Shimura map.

4:10pm-5:00pm, WMAX 216