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Brandt module of ternary quadratic forms
February 14, 2011 (10:00 AM PST - 10:50 AM PST)
Location: Baker Boardroom
MSRI: Baker Board Room
Speaker: Gonzalo Tornaría
Title: The Brandt module of ternary quadratic forms
As proposed by Birch, one can construct partial Brandt matrices by the
method of neighboring lattices for ternary quadratic forms.
In this talk we will present a refinement of the classical notion of
proper equivalence of lattices which leads to the construction of the
full Brandt matrices, at least in the squarefree level case. Moreover
this refinement leads naturally (and is motivated by!) to the
definition of generalized ternary theta series.
We apply these ideas to the construction of modular forms of half
integral weight, giving an explicit version of the Shimura
correspondence which generalizes results of Eichler, Gross, Ponomarev,
Birch, Schulze-Pillot, and Lehman.
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