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Escape of mass on Hilbert modular varieties

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dc.contributor.author Zaman, Asif Ali
dc.date.accessioned 2012-08-30T16:20:46Z
dc.date.available 2012-08-30T16:20:46Z
dc.date.copyright 2012 en_US
dc.date.issued 2012-08-30
dc.identifier.uri http://hdl.handle.net/2429/43097
dc.description.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. en_US
dc.language.iso eng en_US
dc.publisher University of British Columbia en
dc.title Escape of mass on Hilbert modular varieties en_US
dc.type Electronic Thesis or Dissertation en
dc.degree.name Master of Science - MSc en_US
dc.degree.discipline Mathematics en_US
dc.degree.grantor University of British Columbia en
dc.date.graduation 2012-11 en_US
dc.degree.campus UBCV en_US
dc.description.scholarlevel Graduate en


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