Sphere packings centered at S-units of algebraic tori

1992 ◽  
pp. 108-121
Author(s):  
Boris È. Kunyavskii
Keyword(s):  
Sphere Packings ◽  
Algebraic Tori

scholarly journals Diverse densest binary sphere packings and phase diagram

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Ryotaro Koshoji ◽  
Mitsuaki Kawamura ◽  
Masahiro Fukuda ◽  
Taisuke Ozaki
Keyword(s):  
Phase Diagram ◽  
Sphere Packings

scholarly journals On S-class number relations of algebraic tori in Galois extensions of global fields

1991 ◽  
Vol 124 ◽  
pp. 133-144 ◽  
Author(s):  
Masanori Morishita
Keyword(s):  
Class Number ◽  
Quadratic Forms ◽  
Euler Number ◽  
Number Fields ◽  
Binary Quadratic Forms ◽  
Algebraic Number Fields ◽  
Algebraic Tori ◽  
Genus Theory ◽  
Class Number Formula ◽  
Number Formula

As an interpretation and a generalization of Gauss’ genus theory on binary quadratic forms in the language of arithmetic of algebraic tori, Ono [02] established an equality between a kind of “Euler number E(K/k)” for a finite Galois extension K/k of algebraic number fields and other arithmetical invariants associated to K/k. His proof depended on his Tamagawa number formula [01] and Shyr’s formula [Sh] which follows from the analytic class number formula of a torus. Later, two direct proofs were given by Katayama [K] and Sasaki [Sa].

scholarly journals On the jamming phase diagram for frictionless hard-sphere packings

Soft Matter ◽  
2014 ◽  
Vol 10 (39) ◽  
pp. 7838-7848 ◽  
Author(s):  
Vasili Baranau ◽  
Ulrich Tallarek
Keyword(s):  
Phase Diagram ◽  
Hard Sphere ◽  
Sphere Packings
Sign in / Sign up

Export Citation Format

Share Document