---
date: 2022-04-24 19:22
modification date: Sunday 24th April 2022 19:22:56
title: "special values of L functions"
aliases: [special values of L functions]
---

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

---
- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [arithmetic cohomology](arithmetic%20cohomology.md)
	- [Heegner point](Heegner%20point)

---

# special values of L functions

Relation to [automorphic forms](automorphic%20forms) and [motives](Unsorted/motive%20MOC.md):
![](attachments/Pasted%20image%2020220424192259.png)
![](attachments/Pasted%20image%2020220424192335.png)

Computation in [Hodge cohomology](Hodge%20cohomology) using the [plectic conjecture](Unsorted/plectic%20conjecture.md), for [abelian characters](abelian%20characters) of [CM fields](Unsorted/CM%20field.md) and [Hilbert modular forms](Hilbert%20modular%20forms).
![](attachments/Pasted%20image%2020220424192658.png)
![](attachments/Pasted%20image%2020220424192749.png)
![](attachments/Pasted%20image%2020220424192807.png)
Yields a definition of a category of [mixed Hodge structures](Unsorted/pure%20Hodge%20structure.md):
![](attachments/Pasted%20image%2020220424192917.png)
Expected to exist for [arithmetic cohomology](Unsorted/arithmetic%20cohomology.md) of a [Shimura variety](Unsorted/Shimura%20variety.md), using [toroidal compactification](toroidal%20compactification)
![](attachments/Pasted%20image%2020220424192946.png)
![](attachments/Pasted%20image%2020220424193015.png)
See [Tannakian](Unsorted/Tannakian.md) categories.