Weyl's Law with Error Estimate
classification
✦ hep-th
keywords
lambdacusperrorformsproofspacewallaceweyl
read the original abstract
Let X=Sl(3,Z)\Sl(3,R)/SO(3,R). Let N(lambda) denote the dimension of the space of cusp forms with Laplace eigenvalue less than lambda. We prove that N(lambda)=C lambda^(5/2)+O(lambda^2) where C is the appropriate constant establishing Weyl's law with a good error term for the noncompact space X. The proof uses the Selberg trace formula in a form that is modified from the work of Wallace and also draws on results of Stade and Wallace and techniques of Huntley and Tepper. We also, in the course of the proof, give an upper bound on the number of cusp forms that can violate the Ramanujan conjecture.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.