Classification of Countably Infinite Hermitian Forms Over Skewfields

1974 ◽  
Vol 96 (1) ◽  
pp. 145 ◽  
Author(s):  
George Maxwell
Keyword(s):  
Hermitian Forms ◽  
Countably Infinite

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.

Analytic sets having incomparable kleene degrees

1982 ◽  
Vol 47 (4) ◽  
pp. 860-868 ◽  
Author(s):  
Galen Weitkamp
Keyword(s):  
Set Theory ◽  
Characteristic Functions ◽  
Primary Concern ◽  
Descriptive Set Theory ◽  
Upper Semilattice ◽  
Definable Sets ◽  
Analytic Sets ◽  
Countably Infinite ◽  
Descriptive Set

One concern of descriptive set theory is the classification of definable sets of reals. Taken loosely ‘definable’ can mean anything from projective to formally describable in the language of Zermelo-Fraenkel set theory (ZF). Recursiveness, in the case of Kleene recursion, can be a particularly informative notion of definability. Sets of integers, for example, are categorized by their positions in the upper semilattice of Turing degrees, and the algorithms for computing their characteristic functions may be taken as their defining presentations. In turn it is interesting to position the common fauna of descriptive set theory in the upper semilattice of Kleene degrees. In so doing not only do we gain a perspective on the complexity of those sets common to the study of descriptive set theory but also a refinement of the theory of analytic sets of reals. The primary concern of this paper is to calculate the relative complexity of several notable coanalytic sets of reals and display (under suitable set theoretic hypothesis) several natural solutions to Post's problem for Kleene recursion.For sets of reals A and B one says A is Kleene recursive in B (written A ≤KB) iff there is a real y so that the characteristic function XA of A is recursive (in the sense of Kleene [1959]) in y, XB and the existential integer quantifier ∃; i.e. there is an integer e so that XA(x) ≃ {e}(x, y, XB, ≃). Intuitively, membership of a real x ϵ ωω in A can be decided from an oracle for x, y and B using a computing machine with a countably infinite memory and an ability to search and manipulate that memory in finite time. A set is Kleene semirecursive in B if it is the domain of an integer valued partial function recursive in y, XB and ≃ for some real y.

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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