2009 Number Theory Seminar - 12

  • Date: 04/02/2009
Alia Hamieh (UBC)

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