Supercuspidal Representations and Poincare Series over Function Fields

1993 ◽  
Vol 340 (1) ◽  
pp. 395
Author(s):  
Daniel Bump ◽  
Shuzo Takahashi
Keyword(s):  
Function Fields ◽  
Poincaré Series ◽  
Poincare Series ◽  
Supercuspidal Representations

Theta Series, Eisenstein Series and Poincaré Series over Function Fields

2004 ◽  
Vol 56 (2) ◽  
pp. 406-430 ◽  
Author(s):  
Ambrus Pál
Keyword(s):  
Eisenstein Series ◽  
Finite Fields ◽  
Function Fields ◽  
Theta Series ◽  
Poincaré Series ◽  
Poincare Series ◽  
Basic Properties

AbstractWe construct analogues of theta series, Eisenstein series and Poincaré series for function fields of one variable over finite fields, and prove their basic properties.

scholarly journals Poincaré series, 3d gravity and averages of rational CFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Viraj Meruliya ◽  
Sunil Mukhi ◽  
Palash Singh
Keyword(s):  
Poincaré Series ◽  
Simons Theory ◽  
Partition Functions ◽  
Moody Algebra ◽  
Modular Invariant ◽  
Poincare Series ◽  
Single Genus ◽  
3D Gravity ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We investigate the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)k WZW models provide unitary examples for which the Poincaré series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT’s sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU(N)1 and SU(3)k, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions — the latter corresponding to analogues of 3-manifold “wormholes” — such that the expected average is correctly reproduced.

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