Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds

2011/07/13 by Guillarmou, Colin, Naud, Frederic
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1107.2655

Abstract

For convex co-compact hyperbolic manifolds Γ\backslash ℍⁿ⁺¹ for which the dimension of the limit set satisfies δ_Γ< n/2, we show that the high-frequency Eisenstein series associated to a point ξ "at infinity" concentrate microlocally on a measure supported by (the closure of) the set of points in the unit cotangent bundle corresponding to geodesics ending at ξ. The average in ξ of these limit measures equidistributes towards the Liouville measure.

Related

• On the nodal lines of Eisenstein series on Schottky surfaces
• Equidistribution of horospheres on moduli spaces of hyperbolic surfaces
• Quantitative Equidistribution on Hyperbolic Surfaces and Arithmetic Applications
• The L² restriction of the Eisenstein series to a geodesic segment
• On distribution of poles of Eisenstein series and the length spectrum of hyperbolic manifolds