scholarly journals A Note on the Algebraic Growth Rate of Poincaré Series for Kleinian Groups

2011 ◽  
pp. 237-245 ◽  
Author(s):  
Marc Kesseböhmer ◽  
Bernd O. Stratmann
Keyword(s):  
Growth Rate ◽  
Poincaré Series ◽  
Kleinian Groups ◽  
Poincare Series

scholarly journals The exponent of convergence of Poincaré series on some Kleinian groups

1980 ◽  
Vol 32 (3) ◽  
pp. 447-452 ◽  
Author(s):  
Tohru Akaza ◽  
Harushi Furusawa
Keyword(s):  
Poincaré Series ◽  
Kleinian Groups ◽  
Exponent Of Convergence ◽  
Poincare Series

scholarly journals Kleinian groups with unbounded limit sets

1972 ◽  
Vol 13 (1) ◽  
pp. 24-28
Author(s):  
A. F. Beardon
Keyword(s):  
Limit Point ◽  
Automorphic Forms ◽  
Poincaré Series ◽  
Kleinian Groups ◽  
Limit Sets ◽  
Poincare Series ◽  
Crucial Step ◽  
Ordinary Point ◽  
Image Position ◽  
Automorphic Functions

The easiest way to construct automorphic functions is by means of the Poincaré series. If G is a Kleinian group with ∞ an ordinary point of G and if k ≧ 4, thenwhere Vz=(az+b)/(cz+d) and ad-bc=1. The convergence of this series is the crucial step in showing that the Poincaré series converges and is an automorphic form on G If ∞ is a limit point of ∞ the series in (1) may diverge and one can derive automorphic forms on ∞ from the Poincaré series of some conjugate group. These constructions are described in greater detail in /3, pp. 155–165].

Poincaré series for Kleinian groups

1973 ◽  
Vol 26 (5-6) ◽  
pp. 667-672 ◽  
Author(s):  
Lipman Bers
Keyword(s):  
Poincaré Series ◽  
Kleinian Groups ◽  
Poincare Series

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.

Two Applications of Change of Rings Theorems for Poincare-Series

1979 ◽  
Vol 73 (2) ◽  
pp. 163
Author(s):  
Jurgen Herzog ◽  
Manfred Steurich
Keyword(s):  
Poincaré Series ◽  
Poincare Series

scholarly journals Poincaré series for filtrations defined by discrete valuations with arbitrary center

2013 ◽  
Vol 377 ◽  
pp. 66-75 ◽  
Author(s):  
Antonio Campillo ◽  
Ann Lemahieu
Keyword(s):  
Poincaré Series ◽  
Poincare Series

Semigroup and Poincaré series for a finite set of divisorial valuations

2014 ◽  
Vol 28 (1) ◽  
pp. 191-225 ◽  
Author(s):  
Leen Van Langenhoven ◽  
Willem Veys
Keyword(s):  
Poincaré Series ◽  
Poincare Series ◽  
Finite Set ◽  
Divisorial Valuations
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