The Spectra of Some Arithmetical Matrices

Explore the spectral analysis of GCD matrices in this 53-minute seminar talk from the Spectral Geometry in the clouds series. Delve into the fascinating world of arithmetical matrices, focusing on those whose entries are determined by the greatest common divisor of their row and column indices. Discover how this classical topic has gained renewed interest among analysts due to its connections with analytic number theory. Learn about the known results and current research in this field, presented by Alexander Pushnitski from the Centre de recherches mathématiques (CRM). Gain insights into the properties and behavior of these matrices, their spectral characteristics, and their relevance to modern mathematical inquiries.