On generalized length spectrum in quotients of SL4

Abstract

Abstract In this paper we consider a generalized length spectrum in the case of compact symmetric spaces generated as quotients of the special linear group of order four over real numbers. While the classical length spectrum is given as an estimate for a yes function counting prime geodesics of appropriate length, its generalized form is usually represented by a higher order counting function of Chebyshev type. Our goal is to prove that the error term that appears in the classical case in this setting can be significantly improved when derived via analogous, generalized apparatus.