The Brandt module of ternary quadratic lattices
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Date
2005
Authors
Tornaría López, Gonzalo
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Abstract
Given 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.
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