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Let $Q\colon \mathbb{Z}^{n}\oplus\mathbb{Z}^m\to\mathbb{R}$ be a real quadratic form, which we denote $Q(x,y)$, $x\in\mathbb{Z}^n$, $y\in\mathbb{Z}^m$. Suppose: The minimum of $Q(x,y)$ as $y$ varies ...

I am able to prove the following two propositions: Recall that the $i$-th successive minimum of $L\in \mathcal L$, denoted $\lambda_i(L)$ is the infimum of the radii of the balls containing $i$-...

Recall that the $i$-th successive minimum of $L\in \mathcal L$ (space of full rank lattices in $\mathbb R^d$), denoted $\lambda_i(L)$ is the infimum of the radii of the balls containing $i$-linearly ...

Let $\mu$ be the Haar measure defined on the space of unimodular lattices, identified with $\text{SL}(d,\mathbb R)/\text{SL}(d,\mathbb Z)$. The classical Siegel's formula in geometry of numbers states ...

Let $f:\mathbb R^n\to \mathbb R$ be a nonnegative Borel measurable function, and let $f^*$ be the function obtained from $f$ by spherical symmetrization (see Rogers' paper: number of lattice points in ...