Go to  Advanced Search

Escape of mass on Hilbert modular varieties

Show full item record

Files in this item

Files Size Format Description   View
ubc_2012_fall_zaman_asif.pdf 729.7Kb Adobe Portable Document Format   View/Open
Title: Escape of mass on Hilbert modular varieties
Author: Zaman, Asif Ali
Degree: Master of Science - MSc
Program: Mathematics
Copyright Date: 2012
Issue Date: 2012-08-30
Publisher University of British Columbia
Abstract: Let F be a number field, G = PGL(2,F_∞), and K be a maximal compact subgroup of G. We eliminate the possibility of escape of mass for measures associated to Hecke-Maaß cusp forms on Hilbert modular varieties, and more generally on congruence locally symmetric spaces covered by G/K, hence enabling its application to the non-compact case of the Arithmetic Quantum Unique Ergodicity Conjecture. This thesis generalizes work by Soundararajan in 2010 eliminating escape of mass for congruence surfaces, including the classical modular surface SL(2,Z)\H², and follows his approach closely. First, we define M, a congruence locally symmetric space covered by G/K, and articulate the details of its structure. Then we define Hecke-Maass cusp forms and provide their Whittaker expansion along with identities regarding the Whittaker coefficients. Utilizing these identities, we introduce mock P-Hecke multiplicative functions and bound a key related growth measure following Soundararajan’s paper. Finally, amassing our results, we eliminate the possibility of escape of mass for Hecke-Maass cusp forms on M.
Affiliation: Science, Faculty of
URI: http://hdl.handle.net/2429/43097
Scholarly Level: Graduate

This item appears in the following Collection(s)

Show full item record

UBC Library
1961 East Mall
Vancouver, B.C.
Canada V6T 1Z1
Tel: 604-822-6375
Fax: 604-822-3893