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 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 Enhanced equivariant Saito duality

2018 ◽  
Vol 17 (10) ◽  
pp. 1850181
Author(s):  
Wolfgang Ebeling ◽  
Sabir M. Gusein-Zade
Keyword(s):  
Fourier Transform ◽  
Finite Group ◽  
Zeta Functions ◽  
Analytic Formula ◽  
Burnside Ring ◽  
Euler Characteristics ◽  
Dual Pairs ◽  
A Finite Group ◽  
Equivariant Version ◽  
Burnside Rings

In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. Here, a so-called enhanced Burnside ring [Formula: see text] of a finite group [Formula: see text] is defined. An element of it is represented by a finite [Formula: see text]-set with a [Formula: see text]-equivariant transformation and with characters of the isotropy subgroups associated to all points. One gives an enhanced version of the equivariant Saito duality. For a complex analytic [Formula: see text]-manifold with a [Formula: see text]-equivariant transformation of it one has an enhanced equivariant Euler characteristic with values in a completion of [Formula: see text]. It is proved that the (reduced) enhanced equivariant Euler characteristics of the Milnor fibers of Berglund–Hübsch dual invertible polynomials are enhanced dual to each other up to sign. As a byproduct, this implies the result about the orbifold zeta functions of Berglund–Hübsch–Henningson dual pairs obtained earlier.

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

Very Exceptional Group

2014 ◽  
Vol 1006-1007 ◽  
pp. 1071-1075
Author(s):  
Xiao Yu Liang ◽  
Xin Zhang
Keyword(s):  
Finite Group ◽  
Zeta Function ◽  
Nilpotent Group ◽  
Galois Extension ◽  
Prime Order ◽  
Zeta Functions ◽  
Number Fields ◽  
Galois Groups ◽  
Exceptional Group ◽  
A Finite Group

<p>A finite group is called exceptional if for a Galois extension of number fields with the Galois groups , the zeta function of between and does not appear in the Brauer-Kuroda relation of the Dedekind zeta functions. Furthermore, a finite group is called very exceptional if its nontrivial subgroups are all exceptional. In this paper，a Nilpotent group is very exceptional if and only if it has a unique subgroup of prime order for each divisor of .</p>

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 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

On the minimal dimension of a homology sphere on which a finite group acts

2008 ◽  
Vol 144 (2) ◽  
pp. 397-401 ◽  
Author(s):  
BRUNO P. ZIMMERMANN
Keyword(s):  
Finite Group ◽  
Analogous Result ◽  
Simple Groups ◽  
Homology Sphere ◽  
Finite Simple Groups ◽  
Metacyclic Group ◽  
Linear Action ◽  
Minimal Dimension ◽  
A Finite Group

AbstractWe show that the minimal dimension of a faithful action of a metacyclic group$\Z_p \rtimes \Z_q$, for primespandq, on a homology sphere coincides with the minimal dimension of a faithful linear action on a sphere; as a consequence, we obtain the analogous result for various finite simple groups.

EQUIVALENCE RELATIONS ON IMPLICATION-BASED FUZZY AUTOMATON OVER A FINITE GROUP

2020 ◽  
Vol 9 (10) ◽  
pp. 8869-8881
Author(s):  
M. Selvarathi
Keyword(s):  
Finite Group ◽  
Equivalence Relations ◽  
Fuzzy Automaton ◽  
A Finite Group
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