Skip to main content

The Ramanujan Conjecture for Genus two Siegel modular Forms

  • 945 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1968)

Abstract

In this chapter we apply the results obtained in Chaps. 1 and 2 and work of Kottwitz in the special case of the symplectic group of similitudes GSp(4). The main result obtained in this chapter is the proof of the Ramanujan conjecture for GSp(4) for cohomological automorphic forms which are not cuspidal representations associated with parabolic subgroups (CAP). We will assume certain statements regarding the trace formula, the proof of which occupies Chaps. 6–10.

For the moment let G be a connected reductive group over Q, whose derived group is simply connected. Assume that the maximal Q-split torus AG in the center coincides with the maximal R-split torus in the center. Let KG(Afin) be a sufficiently small compact open subgroup (see Sect. 2.2).

Keywords

  • Discrete Series
  • Outer Automorphism
  • Automorphic Representation
  • Fundamental Lemma
  • Siegel Modular Form

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rainer Weissauer .

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Weissauer, R. (2009). The Ramanujan Conjecture for Genus two Siegel modular Forms. In: Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds. Lecture Notes in Mathematics(), vol 1968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89306-6_3

Download citation