scholarly journals Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms II

2014 ◽  
Vol 21 (2) ◽  
pp. 363-378 ◽  
Author(s):  
Yasuo Ohno ◽  
Takashi Taniguchi
Keyword(s):  
Dirichlet Series ◽  
Class Numbers ◽  
Cubic Forms

Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms

2009 ◽  
Vol 131 (6) ◽  
pp. 1525-1541 ◽  
Author(s):  
Yasuo Ohno ◽  
Takashi Taniguchi ◽  
Satoshi Wakatsuki
Keyword(s):  
Dirichlet Series ◽  
Class Numbers ◽  
Cubic Forms

On the relations among the class numbers of binary cubic forms

1998 ◽  
Vol 134 (1) ◽  
pp. 101-138 ◽  
Author(s):  
Jin Nakagawa
Keyword(s):  
Class Numbers ◽  
Cubic Forms

scholarly journals On Dirichlet series whose coefficients are class numbers of binary quadratic forms

1996 ◽  
Vol 142 ◽  
pp. 95-132 ◽  
Author(s):  
Boris A. Datskovsky
Keyword(s):  
Dirichlet Series ◽  
Quadratic Forms ◽  
Positive Definite ◽  
Equivalence Classes ◽  
Class Numbers ◽  
Definite Integral ◽  
Binary Quadratic Forms ◽  
Integral Solutions

For an integer d > 0 (resp. d < 0) let hd denote the number of Sl2(Z)-equivalence classes of primitive (resp. primitive positive-definite) integral binary quadratic forms of discriminant d. For where t and u are the smallest positive integral solutions of the equation t2 − du2 = 4 if d is a non-square and εd = 1 if d is a square.

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]).

On certain Dirichlet series whose coefficients are related to class numbers

1982 ◽  
Vol 179 (2) ◽  
pp. 193-200
Author(s):  
Peter L. Walker
Keyword(s):  
Dirichlet Series ◽  
Class Numbers
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