---
title: lattice
aliases:
  - lattice
  - hyperbolic lattice
  - quadratic space
  - lattices
  - hyperbolic lattices
created: 2022-04-11T23:44:00
updated: 2024-06-23T19:02
links: "[[Hermitian symmetric domains|Hermitian symmetric space]]"
refs: 
---

---
- Refs:
	- Venkatesh lectures <https://www.mit.edu/~fengt/245C_2016.pdf#page=12>
	- [Note with some nice applied background theory](a-sieve-algorithm-based-on-overlattices.pdf)
- Links
	- [[Siegel-Eichler]]

---

# lattice

- $\Lambda\dual \da \ts{z\in \Lambda\tensor \RR \st \forall \ell\in \Lambda,\, z\cdot \ell \in \ZZ}$.
- $S^{\perp \Lambda} \da \ts{z\in \Lambda \st \forall s\in S, \, s\cdot z = 0}$.


![](2024-06-23-6.png)

![](Pasted%20image%2020220807000355.png)
![](Pasted%20image%2020220807000413.png)

![](Pasted%20image%2020220531032629.png)

![](Pasted%20image%2020220427092429.png)

![](2023-02-27neimeir.png)

![](2024-06-23-11.png)

[@BP83] --

![](2024-02-24.png)

Index and signature

![](2024-06-23-14.png)


# Examples

![](Pasted%20image%2020220523210444.png)
![](Pasted%20image%2020220523210454.png)

![](Pasted%20image%2020220523210420.png)

# Results

![](2023-03-10Nikulin.png)
![](2023-03-10orthogmilnor.png)


# Examples



![](2024-06-23-13.png)