---
date: 2022-05-28 00:50
modification date: Saturday 28th May 2022 00:50:53
title: "motivic integration"
aliases: [motivic integration]
---

Last modified date: <%+ tp.file.last_modified_date() %>

---

- Tags: 
	- #todo/untagged
- Refs:
	- <https://people.math.wisc.edu/~maxim/motivic.pdf#page=1> #resources/summaries 
- Links:
	- #todo/create-links 

---

# motivic integration


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# Examples

![](attachments/Pasted%20image%2020220528011549.png)
$$
\begin{aligned}
\int_{A} \mathbb{L}^{-\operatorname{ord}_{t} D} \dmu 
&=\sum_{n \geq 1} \frac{(\mathbb{L}-1)}{\mathbb{L}^{n}} \cdot \mathbb{L}^{-n a}\\
&=(\mathbb{L}-1) \cdot \sum_{n \geq 1} \mathbb{L}^{-n(a+1)} \\
&=(\mathbb{L}-1) \cdot \frac{\mathbb{L}^{-(a+1)}}{1-\mathbb{L}^{-(a+1)}} \\
&=\frac{\mathbb{L}-1}{\mathbb{L}^{(a+1)}-1} \\
&=\frac{1}{1+\mathbb{L}+\cdots+\mathbb{L}^{a}} \\
&=\frac{1}{[\mathbb{P}^a]}
\end{aligned}
$$

# Applications

![](attachments/Pasted%20image%2020220806000452.png)