Classification of Hermitian Forms. VI Group Rings

1976 ◽  
Vol 103 (1) ◽  
pp. 1 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Group Rings ◽  
Hermitian Forms

On the classification of Hermitian forms

1972 ◽  
Vol 18 (1-2) ◽  
pp. 119-141 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Hermitian Forms

scholarly journals ENDOSCOPY AND COHOMOLOGY IN A TOWER OF CONGRUENCE MANIFOLDS FOR

2019 ◽  
Vol 7 ◽  
Author(s):  
SIMON MARSHALL ◽  
SUG WOO SHIN
Keyword(s):  
Symmetric Spaces ◽  
Unitary Groups ◽  
Automorphic Representations ◽  
Locally Symmetric Spaces ◽  
Hermitian Forms ◽  
Work In Progress ◽  
Endoscopic Classification

By assuming the endoscopic classification of automorphic representations on inner forms of unitary groups, which is currently work in progress by Kaletha, Minguez, Shin, and White, we bound the growth of cohomology in congruence towers of locally symmetric spaces associated to$U(n,1)$. In the case of lattices arising from Hermitian forms, we expect that the growth exponents we obtain are sharp in all degrees.

MULTIPLICATIVE JORDAN DECOMPOSITION IN GROUP RINGS OF 2, 3-GROUPS

2010 ◽  
Vol 09 (03) ◽  
pp. 483-492 ◽  
Author(s):  
CHIA-HSIN LIU ◽  
D. S. PASSMAN
Keyword(s):  
Finite Groups ◽  
Group Rings ◽  
Integral Group ◽  
Jordan Decomposition ◽  
Integral Group Rings

In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that ℤ[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, while the corresponding 3-groups were almost completely determined by the present authors. Thus, we are concerned here, for the most part, with groups whose order is divisible by 6. As it turns out, there are precisely three nonabelian 2, 3-groups, of order divisible by 6, with ℤ[G] satisfying MJD. These have orders 6, 12, and 24. In view of another result of Hales, Passi and Wilson, this completes a significant portion of the classification of all finite groups with MJD.

scholarly journals On Universal Binary Hermitian Forms

Integers ◽  
2009 ◽  
Vol 9 (1) ◽  
Author(s):  
Scott Duke Kominers
Keyword(s):  
Quadratic Forms ◽  
Complete Classification ◽  
Hermitian Forms

AbstractEarnest and Khosravani, Iwabuchi, and Kim and Park recently gave a complete classification of the universal binary Hermitian forms. We give a unified proof of the universalities of these Hermitian forms, relying upon Ramanujan's list of universal quadratic forms and the Bhargava–Hanke 290-Theorem. Our methods bypass the

On the classification of hermitian forms

1974 ◽  
Vol 23 (3-4) ◽  
pp. 241-260 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Hermitian Forms
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