Characteristic Polynomials in Clifford Algebras and in More General Algebras
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DOI: 10.1007/s00006-019-0944-5
Abstract: This article combines two independent theories: firstly, the algorithm of Faddeev–Leverrier which calculates characteristic polynomials of matrices; secondly, the Descent Theory which, in particular, lets many properties of matrix algebras descend down to Azumaya algebras,… read more here.
Keywords: characteristic polynomials; algebras characteristic; polynomials clifford; algebras general ... See more keywords
On the Correlation Functions of the Characteristic Polynomials of Non-Hermitian Random Matrices with Independent Entries
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DOI: 10.1007/s10955-019-02353-w
Abstract: The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for the… read more here.
Keywords: polynomials non; functions characteristic; characteristic polynomials; correlation functions ... See more keywords
The characteristic polynomials of abelian varieties of higher dimension over finite fields
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DOI: 10.1016/j.jnt.2018.09.014
Abstract: Abstract The characteristic polynomials of abelian varieties over the finite field F q with q = p n elements have a lot of arithmetic and geometric information. They have been explicitly described for abelian varieties… read more here.
Keywords: dimension; polynomials abelian; varieties higher; characteristic polynomials ... See more keywords
Characteristic Polynomials of Complex Random Matrices and Painlevé Transcendents
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DOI: 10.1093/imrn/rnaa111
Abstract: We study expectations of powers and correlation functions for characteristic polynomials of N×N non-Hermitian random matrices. For the 1-point and 2-point correlation function, we obtain several characterizations in terms of Painleve transcendents, both at finite-N… read more here.
Keywords: ginibre ensemble; characteristic polynomials; random matrices; polynomials complex ... See more keywords