Integer-valued quadratic forms and quadratic Diophantine equations.
Shimura, Goro (2006)
Documenta Mathematica
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Shimura, Goro (2006)
Documenta Mathematica
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Luis Arenas-Carmona (2003)
Annales de l'Institut Fourier
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We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.
C. T. C. Wall (1970)
Compositio Mathematica
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Oukhtite, L. (2005)
International Journal of Mathematics and Mathematical Sciences
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Kominers, Scott Duke (2009)
Integers
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Qin, Yujun (2007)
International Journal of Mathematics and Mathematical Sciences
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Gabriele Nebe (2000)
Journal de théorie des nombres de Bordeaux
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Let be a Dedekind domain with field of fractions and a finite group. We show that, if is a ring of -adic integers, then the Witt decomposition map between the Grothendieck-Witt group of bilinear -modules and the one of finite bilinear -modules is surjective. For number fields is also surjective, if is a nilpotent group of odd order, but there are counterexamples for groups of even order.
Tekcan, A. (2005)
Acta Mathematica Universitatis Comenianae. New Series
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Detlev W. Hoffmann (1991)
Manuscripta mathematica
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Gritsenko, V., Hulek, K., Sankaran, G.K. (2007)
Documenta Mathematica
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Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)
Open Mathematics
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Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....