On determinants identity minus Hankel matrix
نویسندگان
چکیده
منابع مشابه
Determinants of Hankel Matrices
The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval. The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.
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In this paper, we compute, for large n, the determinant of a class of n×nHankel matrices, which arise from a smooth perturbation of the Jacobi weight. For this purpose, we employ the same idea used in previous papers, where the unknown determinant Dn[wα,βh] is compared with the known determinant Dn[wα,β]. Here wα,β is the Jacobi weight and wα,βh, where h = h(x), x ∈ [−1, 1], is strictly positiv...
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We study the asymptotics of Hankel determinants constructed using the values ζ(an + b) of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.
متن کاملHankel Determinants of Dirichlet Series
We derive a general expression for the Hankel determinants of a Dirichlet series F (s) and derive the asymptotic behavior for the special case that F (s) is the Riemann zeta function. In this case the Hankel determinant is a discrete analogue of the Selberg integral and can be viewed as a matrix integral with discrete measure. We brie y comment on its relation to Plancherel measures.
متن کاملHankel Determinants of Eisenstein Series
Abstract. In this paper we prove Garvan’s conjectured formula for the square of the modular discriminant ∆ as a 3 by 3 Hankel determinant of classical Eisenstein series E2n. We then obtain similar formulas involving minors of Hankel determinants for E2r∆, for m = 1, 2, 3 and r = 2, 3, 4, 5, 7, and E14∆. We next use Mathematica to discover, and then the standard structure theory of the ring of m...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2019
ISSN: 0024-6093,1469-2120
DOI: 10.1112/blms.12271