On Zeta Functions Associated with Prehomogeneous Vector Spaces

1974 ◽  
Vol 100 (1) ◽  
pp. 131 ◽  
Author(s):  
Mikio Sato ◽  
Takuro Shintani
Keyword(s):  
Zeta Functions ◽  
Vector Spaces ◽  
Prehomogeneous Vector Spaces

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 Modular forms arising from zeta functions in two variables attached to prehomogeneous vector spaces related to quadratic forms

2004 ◽  
Vol 175 ◽  
pp. 1-37 ◽  
Author(s):  
Takahiko Ueno
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Zeta Functions ◽  
Vector Spaces ◽  
Parabolic Subgroups ◽  
Converse Theorem ◽  
Half Integral Weight ◽  
Prehomogeneous Vector Spaces ◽  
Integral Weight ◽  
Weil Type

AbstractIn this paper, we prove the functional equations for the zeta functions in two variables associated with prehomogeneous vector spaces acted on by maximal parabolic subgroups of orthogonal groups. Moreover, applying the converse theorem of Weil type, we show that elliptic modular forms of integral or half integral weight can be obtained from the zeta functions.

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