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Escape of mass on Hilbert modular varieties Zaman, Asif Ali
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.
Item Metadata
Title |
Escape of mass on Hilbert modular varieties
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2012
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Description |
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.
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Genre | |
Type | |
Language |
eng
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Date Available |
2012-08-30
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0073094
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2012-11
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International