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

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

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 Hydride-based antiperovskites with soft anionic sublattices as fast alkali ionic conductors

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Shenghan Gao ◽  
Thibault Broux ◽  
Susumu Fujii ◽  
Cédric Tassel ◽  
Kentaro Yamamoto ◽  
...  
Keyword(s):  
Experimental Studies ◽  
Ionic Conductivities ◽  
Cubic Phase ◽  
Ionic Conductors ◽  
Large Size ◽  
Migration Barriers ◽  
Soft Phonon Mode ◽  
Aliovalent Substitution ◽  
Cubic Forms ◽  
The Ideal

AbstractMost solid-state materials are composed of p-block anions, only in recent years the introduction of hydride anions (1s2) in oxides (e.g., SrVO2H, BaTi(O,H)3) has allowed the discovery of various interesting properties. Here we exploit the large polarizability of hydride anions (H–) together with chalcogenide (Ch2–) anions to construct a family of antiperovskites with soft anionic sublattices. The M3HCh antiperovskites (M = Li, Na) adopt the ideal cubic structure except orthorhombic Na3HS, despite the large variation in sizes of M and Ch. This unconventional robustness of cubic phase mainly originates from the large size-flexibility of the H– anion. Theoretical and experimental studies reveal low migration barriers for Li+/Na+ transport and high ionic conductivity, possibly promoted by a soft phonon mode associated with the rotational motion of HM6 octahedra in their cubic forms. Aliovalent substitution to create vacancies has further enhanced ionic conductivities of this series of antiperovskites, resulting in Na2.9H(Se0.9I0.1) achieving a high conductivity of ~1 × 10–4 S/cm (100 °C).

scholarly journals Class numbers and self-conjugate 7-cores

2021 ◽  
Vol 180 ◽  
pp. 105427
Author(s):  
Ken Ono ◽  
Wissam Raji
Keyword(s):  
Class Numbers
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