A mass formula for unimodular lattices with no roots
A mass formula for unimodular lattices with no roots
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DOI：
10.1090/s0025-5718-02-01455-2
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发表时间：
2000-12
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通讯作者：
Oliver D. King
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文献类型：
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作者：
Oliver D. King
我们给出了具有任意指定根系的n维么模格的质量公式。我们利用Siegel Eisenstein级数的傅里叶系数的Katsurada公式计算了n≤30维偶么模32维格和奇么模格的所有根系的质量.特别地，我们发现了无根的偶么模32维格的质量，以及在维n≤30中没有根的奇么模格的质量，从而验证了Bacher和Venkov在27和28维的计数。与Minkowski-Siegel质量常数相比，我们还计算了26到30维不等价么模格的个数的更好的下界。
We derive a mass formula for n-dimensional unimodular lattices having any prescribed root system. We use Katsurada's formula for the Fourier coefficients of Siegel Eisenstein series to compute these masses for all root systems of even unimodular 32-dimensional lattices and odd unimodular lattices of dimension n ≤ 30. In particular, we find the mass of even unimodular 32- dimensional lattices with no roots, and the mass of odd unimodular lattices with no roots in dimension n ≤ 30, verifying Bacher and Venkov's enumerations in dimensions 27 and 28. We also compute better lower bounds on the number of inequivalent unimodular lattices in dimensions 26 to 30 than those afforded by the Minkowski-Siegel mass constants.