Skip navigation
Please use this identifier to cite or link to this item:
Title: Equidistribution in Shrinking Sets and L^4-Norm Bounds for Automorphic Forms
Authors: Humphries, Peter
Advisors: Sarnak, Peter C
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2017
Publisher: Princeton, NJ : Princeton University
Abstract: This thesis deals with two closely related problems stemming from the random wave conjecture for Maaß forms. The first problem is quantum unique ergodicity in shrinking sets; we show that by averaging over the centre of hyperbolic balls in Γ\H, quantum unique ergodicity holds for almost every shrinking ball whose radius is larger than the Planck scale. This result is conditional on the generalised Lindelöf hypothesis for Maaß eigenforms but is unconditional for Eisenstein series. We also show that equidistribution for Maaß eigenforms need not hold at or below the Planck scale. The second problem is bounding the L^4-norm of a Maaß form in the large eigenvalue limit; we complete the work of Spinu to show that the L^4-norm of an Eisenstein series E(z,1/2+it_g) restricted to compact sets is bounded by sqrt{log t_g}.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

Files in This Item:
File Description SizeFormat 
Humphries_princeton_0181D_12203.pdf712.58 kBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.