Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Number Theory

arXiv:0908.0699 (math)
[Submitted on 5 Aug 2009 (v1), last revised 12 Nov 2009 (this version, v4)]

Title:On the tempered L-function conjecture

Authors:Volker Heiermann, Eric Opdam
View PDF
Abstract: We give a general proof of Shahidi's tempered L-function conjecture, which has previously been known in all but one case. One of the consequences is the standard modules conjecture for p-adic groups, which means that the Langlands quotient of a standard module is generic if and only if the standard module is irreducible and the inducing data generic. We have also included the result that every generic tempered representation of a p-adic group is a sub-representation of a representation parabolically induced from a generic supercuspidal representation with a non-negative real central character.
Comments: 19 pages, 13 figures, minor misleading misprints corrected and an address updated
Subjects: Number Theory (math.NT); Representation Theory (math.RT)
MSC classes: 11F66, 11F70, 22E55
Cite as: arXiv:0908.0699 [math.NT]
  (or arXiv:0908.0699v4 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.0908.0699

Submission history

From: Volker Heiermann [view email]
[v1] Wed, 5 Aug 2009 16:10:48 UTC (39 KB)
[v2] Fri, 28 Aug 2009 18:12:28 UTC (39 KB)
[v3] Tue, 1 Sep 2009 06:36:47 UTC (39 KB)
[v4] Thu, 12 Nov 2009 21:58:51 UTC (39 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2009-08
Change to browse by:
math
math.RT

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)