Analysis of the spectrum of SL(3,Z)/SL(3,R)/SO(3,R).

Title: Analysis of the spectrum of SL(3,Z)/SL(3,R)/SO(3,R).
Identifier: AAI9997112
identifier: 9997112
Creator: Moh, Nam-Jong.
Contributor: Adviser: Jonathan Huntley
Date: 2001
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In this thesis we make a systematic study of the spectral properties of the space SL(3,Z)\SL(3,R)/SO(3,R). In particular we use Rayleigh quotient method to give a lower bound for the first non-trivial eigenvalue of the Laplace-Beltrami operator, we use the Selberg trace formula to obtain Weyl's law with an error term and we make a detailed study of Whittaker functions to obtain a comparison test that allows one to determine when two cusp forms are the same if sufficiently many Fourier coefficients agree. We conclude by showing what would be true if conjectures related to the Riemann hypothesis were true.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.