论文标题
在平均值公式上，用于晶格的多个金额及其双重公式
On a mean value formula for multiple sums over a lattice and its dual
论文作者
论文摘要
我们证明了罗杰斯在$ r^n $中的单模型晶格中的Rogers的平均值公式的广义版本，该版本的平均值比晶格$ l $及其dual $ l^*$具有多值的平均值。作为应用程序，我们证明，对于$ l $，相对于sl $（n，r）$ - 不变的概率度量，在大尺寸$ n $的限制下，由非零矢量$ \ pm x $ in L的长度确定的量，一方面是零零的$ \ pm pm x'$ flys of pm x'$ \ l^y y y $ \ l^*线，强度为1/2。
We prove a generalized version of Rogers' mean value formula in the space $X_n$ of unimodular lattices in $R^n$, which gives the mean value of a multiple sum over a lattice $L$ and its dual $L^*$. As an application, we prove that for $L$ random with respect to the SL$(n,R)$-invariant probability measure, in the limit of large dimension $n$, the volumes determined by the lengths of the non-zero vectors $\pm x$ in L on the one hand, and the non-zero vectors $\pm x'$ in $L^*$ on the other hand, converge weakly to two independent Poisson processes on the positive real line, both with intensity 1/2.
