scholarly journals Zeta Functions in Several Variables Associated with Prehomogeneous Vector Spaces III: Eisenstein Series for Indefinite Quadratic Forms

1982 ◽  
Vol 116 (1) ◽  
pp. 177 ◽  
Author(s):  
Fumihiro Sato
Keyword(s):  
Eisenstein Series ◽  
Quadratic Forms ◽  
Zeta Functions ◽  
Vector Spaces ◽  
Several Variables ◽  
Prehomogeneous Vector Spaces ◽  
Indefinite Quadratic

scholarly journals On zeta functions associated with quadratic forms of variable coefficients

1979 ◽  
Vol 73 ◽  
pp. 117-147 ◽  
Author(s):  
Toshiaki Suzuki
Keyword(s):  
General Theory ◽  
Quadratic Forms ◽  
Zeta Functions ◽  
Variable Coefficients ◽  
The Other ◽  
Class Numbers ◽  
Vector Spaces ◽  
Prehomogeneous Vector Spaces ◽  
Indefinite Quadratic ◽  
Cubic Forms

In 1938, C. L. Siegel studied zeta functions of indefinite quadratic forms ([6], c). On the other hand, M. Sato and T. Shintani constructed the general theory of zeta functions of one complex variable associated with prehomogeneous vector spaces in 1974 ([1]). Moreover T. Shintani studied several zeta functions of prehomogeneous vector spaces, especially, “Dirichlet series whose coefficients are class-numbers of integral binary cubic forms” ([3]) and “Zeta functions associated with the vector space of quadratic forms” ([2]).

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.

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
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