Asymptotic Structure of Eigenvalues and Eigenvectors of Certain Triangular Hankel Matrices
Yu. V. Matiyasevich · Doklady Mathematics · 2022
Abstract The Hankel matrices considered in this article arose in one reformulation of the Riemann hypothesis proposed earlier by the author. Computer calculations showed that, in the case of the Riemann zeta function, the eigenvalues and the eigenvectors of such matrices have an interesting structure. The article studies a model situation when the zeta function is replaced by a function having a single zero. For this case, we indicate the first terms of the asymptotic expansions of the smallest and largest (in absolute value) eigenvalues and the corresponding eigenvectors.