Asymptotic expansions of the non-holomorphic Eisenstein series II

摘要

This report is revised version of [8J (2002). We describe one asymptotic formula of the non-holomorphic Eisenstein series for Shi(Z) on the critical line by using Airy functions. The f-aspect of the Eisenstein series is not simple contrary to the good behavior of its constant term. We employ uniform expansions of the Bessel function due to Olver derived from the theory of asymptotic solutions of differential equations. Our result is maybe regarded as Voronoi-Atkinson type formula.