The Brandt module of ternary quadratic lattices

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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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