A characterization of the Z^n lattice
A characterization of the Z^n lattice
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Z^n 晶格的表征
DOI：
10.4310/mrl.1995.v2.n3.a9
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
N. Elkies
中科院分区：
文献类型：
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作者：
N. Elkies
利用θ级数和模形式证明了Z^n是唯一不含范数<n的特征向量的秩为n的整幺模格，即唯一不含向量w使得（w，w）<n且2|（v，v+w）的所有格向量v.通过工作的克朗海默和其他人的塞伯格-威滕方程这产生了另一种证明定理的唐纳森的几何形状的4-流形。
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.