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
Unimodality and peak location of the characteristic polynomials of two distance matrices of trees
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DOI: 10.1007/s40314-025-03163-5
Abstract: Unimodality of the normalized coefficients of the characteristic polynomials of distance matrices of trees are known and bounds on the location of its peak (the largest coefficient) are also known. Recently, an extension of these… read more here.
Keywords: characteristic polynomials; distance; distance matrices; location ... 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
p-Adic quotient sets: Linear recurrence sequences with reducible characteristic polynomials
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DOI: 10.4153/s0008439524000547
Abstract: Abstract Let $(x_n)_{n\geq 0}$ be a linear recurrence sequence of order $k\geq 2$ satisfying $$ \begin{align*}x_n=a_1x_{n-1}+a_2x_{n-2}+\dots+a_kx_{n-k}\end{align*} $$ for all integers $n\geq k$ , where $a_1,\dots ,a_k,x_0,\dots , x_{k-1}\in \mathbb {Z},$ with $a_k\neq 0$ . In… read more here.
Keywords: characteristic polynomials; linear recurrence; adic quotient; recurrence sequences ... See more keywords