Poincaré series and zeta functions for surface group actions on ℝ-trees

1997 ◽  
Vol 226 (3) ◽  
pp. 335-347
Author(s):  
Mark Pollicott ◽  
Richard Sharp
Keyword(s):  
Group Actions ◽  
Zeta Functions ◽  
Surface Group ◽  
Poincaré Series ◽  
Poincare Series

scholarly journals EQUIVARIANT ZETA FUNCTIONS FOR INVARIANT NASH GERMS

2016 ◽  
Vol 222 (1) ◽  
pp. 100-136 ◽  
Author(s):  
FABIEN PRIZIAC
Keyword(s):  
Finite Group ◽  
Zeta Functions ◽  
Poincaré Series ◽  
Linear Action ◽  
Poincare Series ◽  
Motivic Zeta Functions ◽  
A Finite Group

To any Nash germ invariant under right composition with a linear action of a finite group, we associate its equivariant zeta functions, inspired from motivic zeta functions, using the equivariant virtual Poincaré series as a motivic measure. We show Denef–Loeser formulas for the equivariant zeta functions and prove that they are invariants for equivariant blow-Nash equivalence via equivariant blow-Nash isomorphisms. Equivariant blow-Nash equivalence between invariant Nash germs is defined as a generalization involving equivariant data of the blow-Nash equivalence.

scholarly journals Motivic zeta functions for curve singularities

2010 ◽  
Vol 198 ◽  
pp. 47-75 ◽  
Author(s):  
J. J. Moyano-Fernández ◽  
W. A. Zúňiga-Galindo
Keyword(s):  
Functional Equation ◽  
Zeta Function ◽  
Local Ring ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Zeta Functions ◽  
Poincaré Series ◽  
Poincare Series ◽  
Motivic Zeta Functions ◽  
Curve Singularities

AbstractLet X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring Op,x at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if Op,x is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincaré series introduced by Campillo, Delgado, and Gusein-Zade.

scholarly journals Equivariant Poincaré Series and Monodromy Zeta Functions of Quasihomogeneous Polynomials

2012 ◽  
Vol 48 (3) ◽  
pp. 653-660 ◽  
Author(s):  
Wolfgang Ebeling ◽  
Sabir Gusein-Zade
Keyword(s):  
Zeta Functions ◽  
Poincaré Series ◽  
Poincare Series

scholarly journals Motivic zeta functions for curve singularities

2010 ◽  
Vol 198 ◽  
pp. 47-75
Author(s):  
J. J. Moyano-Fernández ◽  
W. A. Zúňiga-Galindo
Keyword(s):  
Functional Equation ◽  
Zeta Function ◽  
Local Ring ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Zeta Functions ◽  
Poincaré Series ◽  
Poincare Series ◽  
Motivic Zeta Functions ◽  
Curve Singularities

AbstractLetXbe a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristicpbig enough. Given a local ringOp,x at a rational singular pointPofX, we attached a universal zeta function which is a rational function and admits a functional equation ifOp,x is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincaré series introduced by Campillo, Delgado, and Gusein-Zade.

scholarly journals Twisted Poincaré series and zeta functions on finite quotients of buildings

2018 ◽  
Vol 49 (3) ◽  
pp. 309-336
Author(s):  
Ming-Hsuan Kang ◽  
Rupert McCallum
Keyword(s):  
Zeta Functions ◽  
Poincaré Series ◽  
Poincare Series ◽  
Finite Quotients

scholarly journals An equivariant Poincaré series of filtrations and monodromy zeta functions

2014 ◽  
Vol 28 (2) ◽  
pp. 449-467 ◽  
Author(s):  
A. Campillo ◽  
F. Delgado ◽  
S. M. Gusein-Zade
Keyword(s):  
Zeta Functions ◽  
Poincaré Series ◽  
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
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