Approximate Formulas for Zeta Functions of Selberg’s Type in Quotients of SL4

The goal of the paper is to derive some approximate formulas for the logarithmic derivative of several zata functions of Selberg’s type for compact symmetric spaces formed as quotients of the Lie group SL4 (R). Such formulas, known in literature as Tutchmarsh-Landau style approximate formulas, are usually applied in order to obtain prime geodesic theorems in various settings of underlying locally symmetric spaces.

On some recent progress in the classification of $$(P\hbox { and }Q)$$-polynomial association schemes

The problem of classification of $$(P\hbox { and }Q)$$(PandQ)-polynomial association schemes, as a finite analogue of E. Cartan’s classification of compact symmetric spaces, was posed in the monograph “Association schemes” by E. Bannai and T. Ito in the early 1980s. In this expository paper, we report on some recent results towards its solution.