On the error term in the prime geodesic theorem for SL4
In this paper we pay our particular attention to the error term in the prime geodesic theorem for compact symmetric spaces represented as double coset spaces of the special linear group of order four over real numbers. It is known that in the case of compact locally symmetric Riemannian manifolds of strictly negative sectional curvature, the corresponding error term depends on classification of Riemannian symmetric spaces of real rank one. In particular, the error term is a function depending on the dimension of the underlying locally symmetric space. In this research we prove that the error term in the case at hand is a function depending on the degree of the polynomial that appears in the functional equation of the corresponding Selberg zeta function.