Poincaré Series Operator with Petersson Inner Product

2000 ◽  
pp. 1207-1211
Author(s):  
Gregory M. Lyan ◽  
Gyungsoo Woo
Keyword(s):  
Poincaré Series ◽  
Inner Product ◽  
Poincare Series

scholarly journals Regularized inner products of meromorphic modular forms and higher Green’s functions

2019 ◽  
Vol 21 (05) ◽  
pp. 1850029
Author(s):  
Kathrin Bringmann ◽  
Ben Kane ◽  
Anna-Maria von Pippich
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Green's Functions ◽  
Green’S Functions ◽  
Poincaré Series ◽  
Independent Interest ◽  
Inner Product ◽  
Poincare Series ◽  
Inner Products

In this paper, we study generalizations of Poincaré series arising from quadratic forms, which naturally occur as outputs of theta lifts. Integrating against them yields evaluations of higher Green’s functions. For this we require a new regularized inner product, which is of independent interest.

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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