Rodriguez-Villegas, Fernando689243892008-08-282017-05-112008-08-282017-05-112005http://hdl.handle.net/2152/2129textGiven a positive definite ternary quadratic lattice Λ, we construct a free module M(Λ) with Hecke action, together with a family of Hecke-linear maps ϑl from M(Λ) to certain spaces of modular forms of half integral weight. The latter are given explicitly by a new kind of generalized theta series, which we prove to be modular with level independent of l. Key to our work is the introduction of a refinement to the classic notion of proper equivalence of lattices.electronicengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.Forms, TernaryForms, QuadraticLattice theoryThesis