Thesis advisor: Dubi Kelmer / We prove a second moment formula for incomplete Eisenstein series on the homogeneous space Γ\G with G the orientation preserving isometry group of the real (n + 1)-dimensional hyperbolic space and Γ⊂ G a non-uniform lattice. This result generalizes the classical Rogers' second moment formula for Siegel transform on the space of unimodular lattices. We give two applications of this moment formula. In Chapter 5 we prove a logarithm law for unipotent flows making cusp excursions in a non-compact finite-volume hyperbolic manifold. In Chapter 6 we study the counting problem counting the number of orbits of Γ-translates in an increasing family of generalized sectors in the light cone, and prove a power saving estimate for the error term for a generic Γ-translate with the exponent determined by the largest exceptional pole of corresponding Eisenstein series. When Γ is taken to be the lattice of integral points, we give applications to the primitive lattice points counting problem on the light cone for a generic unimodular lattice coming from SO₀(n+1,1)(ℤ\SO₀(n+1,1). / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.
| Identifer | oai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_108115 |
| Date | January 2018 |
| Creators | Yu, Shucheng |
| Publisher | Boston College |
| Source Sets | Boston College |
| Language | English |
| Detected Language | English |
| Type | Text, thesis |
| Format | electronic, application/pdf |
| Rights | Copyright is held by the author. This work is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0). |
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