Burnside ring of a Galois group and the relations between zeta functions of intermediate fields

1981 ◽  
pp. 603-610
Author(s):  
D. Husemoller
Keyword(s):  
Galois Group ◽  
Zeta Functions ◽  
Burnside Ring

Zeta functions of twisted modular curves

2006 ◽  
Vol 80 (1) ◽  
pp. 89-103 ◽  
Author(s):  
Cristian Virdol
Keyword(s):  
Zeta Function ◽  
Galois Group ◽  
Complex Plane ◽  
Zeta Functions ◽  
Modular Curves ◽  
Absolute Galois Group ◽  
Modular Curve ◽  
The Absolute

AbstractIn this paper we compute and continue meromorphically to the whole complex plane the zeta function for twisted modular curves. The twist of the modular curve is done by a modprepresentation of the absolute Galois group.

scholarly journals On L-Functions of Twisted 3-Dimensional Quaternionic Shimura Varieties

2008 ◽  
Vol 190 ◽  
pp. 87-104
Author(s):  
Cristian Virdol
Keyword(s):  
Galois Group ◽  
Complex Plane ◽  
Zeta Functions ◽  
Shimura Varieties ◽  
Absolute Galois Group ◽  
3 Dimensional ◽  
Entire Complex ◽  
The Absolute

In this paper we compute and continue meromorphically to the entire complex plane the zeta functions of twisted quaternionic Shimura varieties of dimension 3. The twist of the quaternionic Shimura varieties is done by a mod ℘ representation of the absolute Galois group.

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 Zeta functions of finite Schreier graphs and their zig-zag products

2016 ◽  
Vol 16 (08) ◽  
pp. 1750151
Author(s):  
Asif Shaikh ◽  
Hemant Bhate
Keyword(s):  
Galois Group ◽  
Zeta Functions ◽  
Schreier Graphs ◽  
Definition Of

We investigate the Ihara zeta functions of finite Schreier graphs [Formula: see text] of the Basilica group. We show that [Formula: see text] is two sheeted unramified normal covering of [Formula: see text], for all [Formula: see text] with Galois group [Formula: see text] In fact, for any [Formula: see text], the graph [Formula: see text] is [Formula: see text] sheeted unramified, non-normal covering of [Formula: see text]. In order to do this, we give the definition of the [Formula: see text] [Formula: see text] [Formula: see text] of Schreier graphs of Basilica groups. We also show the corresponding results in zig-zag product of Schreier graphs [Formula: see text] with a [Formula: see text]-cycle.

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