scholarly journals The Igusa local zeta function of the simple prehomogeneous vector space ${(GL(1)^4\times SL(2n+1),\Lambda_2\oplus\Lambda_1\oplus\Lambda_1\oplus\Lambda_1)}$

2005 ◽  
Vol 57 (1) ◽  
pp. 115-126
Author(s):  
Satoshi WAKATSUKI
Keyword(s):  
Vector Space ◽  
Zeta Function ◽  
Local Zeta Function ◽  
Prehomogeneous Vector Space

GLOBAL ZETA FUNCTIONS OF FREUDENTHAL QUARTICS

2002 ◽  
Vol 13 (08) ◽  
pp. 797-820
Author(s):  
HIROSHI SAITO
Keyword(s):  
Vector Space ◽  
Zeta Function ◽  
Explicit Formula ◽  
Explicit Form ◽  
Zeta Functions ◽  
The Other ◽  
Vector Spaces ◽  
Prehomogeneous Vector Space ◽  
Prehomogeneous Vector Spaces

We give two applications of an explicit formula for global zeta functions of prehomogeneous vector spaces in Math. Ann.315 (1999), 587–615. One is concerned with an explicit form of global zeta functions associated with Freudenthal quartics, and the other the comparison of the zeta function of a unsaturated prehomogeneous vector space with that of the saturated one obtained from it.

scholarly journals A new generating function for calculating the Igusa local zeta function

2017 ◽  
Vol 304 ◽  
pp. 355-420 ◽  
Author(s):  
Raemeon A. Cowan ◽  
Daniel J. Katz ◽  
Lauren M. White
Keyword(s):  
Zeta Function ◽  
Generating Function ◽  
Local Zeta Function

scholarly journals On the convergence of the zeta function for certain prehomogeneous vector spaces

1995 ◽  
Vol 140 ◽  
pp. 1-31 ◽  
Author(s):  
Akihiko Yukie
Keyword(s):  
Invariant Measure ◽  
Zeta Function ◽  
Complex Variable ◽  
Vector Spaces ◽  
Invariant Polynomial ◽  
Connected Component ◽  
Relative Invariant ◽  
Prehomogeneous Vector Space ◽  
Prehomogeneous Vector Spaces ◽  
Rational Character

Let (G, V) be an irreducible prehomogeneous vector space defined over a number field k, P ∈ k[V] a relative invariant polynomial, and χ a rational character of G such that . For , let Gx be the stabilizer of x, and the connected component of 1 of Gx. We define L0 to be the set of such that does not have a non-trivial rational character. Then we define the zeta function for (G, Y) by the following integralwhere Φ is a Schwartz-Bruhat function, s is a complex variable, and dg” is an invariant measure.

scholarly journals Poles of the Igusa local zeta function of some hybrid polynomials

2014 ◽  
Vol 25 ◽  
pp. 37-48
Author(s):  
Edwin León-Cardenal ◽  
Denis Ibadula ◽  
Dirk Segers
Keyword(s):  
Zeta Function ◽  
Local Zeta Function

scholarly journals The local zeta function for symmetric spaces of non-compact type

2011 ◽  
Vol 61 (1) ◽  
pp. 125-136 ◽  
Author(s):  
Tomás F. Godoy ◽  
Roberto J. Miatello ◽  
Floyd L. Williams
Keyword(s):  
Zeta Function ◽  
Symmetric Spaces ◽  
Compact Type ◽  
Local Zeta Function
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