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A characterization of the Z^n lattice

Noam D. Elkies
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Abstract

We use theta series and modular forms to prove that Z^n is the only integral unimodular lattice of rank n without characteristic vectors of norm <n, i.e. the only integral unimodular lattice not containing a vector w such that (w,w)<n and 2|(v,v+w) for all lattice vectors v. By the work of Kronheimer and others on the Seiberg-Witten equation this yields an alternative proof of a theorem of Donaldson on the geometry of 4-manifolds.

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Noam D. Elkies. 1999-06-02. A characterization of the Z^n lattice. https://arxiv.org/abs/math/9906019

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