# Tagged Questions

**0**

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42 views

### Number of lattice points inside a parallelogram defined by a vector on the “rhombic plane”

I will give here a specific case and try to explain the question the best I can:
The rhombic plane is the plane with the x-axis the same as the Cartesian plane but the y-axis tilted at $60$ degrees. ...

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86 views

### Siegel's Mean Value Theorem by Rogers and Macbeath

I recently became engaged in the work of Siegel, Schmidt, Rogers, Macbeath regarding random lattices and geometry of numbers, e.g. Siegel proved that
$$\int_{SL(n,\mathbb{R})/SL(n,\mathbb{Z})} \sum_{ ...

**6**

votes

**3**answers

542 views

### Sums of inverse determinants over matrices

Let $A \in M_n(\mathbb Z)$ and $\|A\| = \max |a_{ij}|$.
Denote $$ S(r) = \sum_{\substack{\|A\| \leq r \\\ \det{A} \neq 0}} \dfrac{1}{|\det{A}|} $$
- the sum over all matrices $A \in M_n(\mathbb Z)$ ...