Hankel determinants of a Sturmian sequence

Hankel determinants of the Thue-Morse sequence

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.

Perturbed Hankel determinants

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...

Hankel Determinants of Zeta Values

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.

Hankel 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.