Abstract
Recently Alexandrov, Banerjee, Manschot and Pioline constructed generalizations of Zwegers theta functions for lattices of signature (\(n-2,2\)). Their functions, which depend on two pairs of time like vectors, are obtained by ‘completing’ a non-modular holomorphic generating series by means of a non-holomorphic theta type series involving generalized error functions. We show that their completed modular series arises as integrals of the 2-form valued theta functions, defined in old joint work of the author and John Millson, over a surface S determined by the pairs of time like vectors. This gives an alternative construction of such series and a conceptual basis for their modularity. The holomorphic generating series is interpreted as the series of intersection numbers of the surface S with complex divisors associated to positive lattice vectors.
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References
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