scholarly journals Microlocal analysis and calculations on some relatively invariant hyperfunctions related to zeta functions associated with the vector spaces of quadratic forms

1986 ◽  
Vol 22 (3) ◽  
pp. 395-463 ◽  
Author(s):  
Masakazu Muro
Keyword(s):  
Quadratic Forms ◽  
Zeta Functions ◽  
Microlocal Analysis ◽  
Vector Spaces

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.

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]).

Hardy’s theorem for zeta-functions of quadratic forms

1996 ◽  
Vol 106 (3) ◽  
pp. 217-226 ◽  
Author(s):  
K Ramachandra ◽  
A Sankaranarayanan
Keyword(s):  
Quadratic Forms ◽  
Zeta Functions ◽  
Hardy’S Theorem
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