scholarly journals Asymptotics and Local Constancy of Characters of p-adic Groups

2016 ◽  
pp. 259-295 ◽  
Author(s):  
Ju-Lee Kim ◽  
Sug Woo Shin ◽  
Nicolas Templier
Keyword(s):  
Local Constancy

scholarly journals Explicit Calculations of Automorphic Forms for Definite Unitary Groups

2008 ◽  
Vol 11 ◽  
pp. 326-342 ◽  
Author(s):  
David Loeffler
Keyword(s):  
Unitary Group ◽  
Automorphic Forms ◽  
Galois Representations ◽  
Level Structure ◽  
Unitary Groups ◽  
3 Dimensional ◽  
Local Constancy

I give an algorithm for computing the full space of automor-phic forms for definite unitary groups over ℚ, and apply this to calculate the automorphic forms of level G(hat{Z}) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic form of weight (3, 3) corresponding to a family of 3-dimensional irreducible ℓ-adic Galois representations. I also compute the 2-adic slopes of some automorphic forms with level structure at 2, giving evidence for the local constancy of the slopes.

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