Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
PhD_Thesis (5).pdf (852.27 KB)
ETD Abstract Container
Abstract Header
A Reformulation of the Delta Method and the Subconvexity Problem
Author Info
Leung, Wing Hong
ORCID® Identifier
http://orcid.org/0000-0002-3772-9941
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1650554459410968
Abstract Details
Year and Degree
2022, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
Let P be a prime and k be an even integer. Let f be a full level holomorphic cusp form of weight k and rho be a primitive level P holomorphic cusp form with arbitrary nebentypus and fixed weight kappa. In this thesis, We develop a reformulation of the DFI Delta method to prove a hybrid subconvexity bound for L(1/2,Sym2 f X rho) when P^{1/4+eta} < k < P^{21/17-eta} for any 0 < eta < 67/136. In the exploration of the Delta method, we also show the Weyl bound for GL(2) in t-aspect for a holomorphic or Hecke-Maass cusp form of arbitrary level and nebentypus using a multiplicative Delta method. Related to the L-function L(1/2,Sym2 f X rho), we also establish a reduction of holomorphic Quantum Unique Ergodicity into a lengthened shifted sum.
Committee
Roman Holowinsky (Advisor)
Wenzhi Luo (Committee Member)
James Cogdell (Committee Member)
Pages
187 p.
Subject Headings
Mathematics
Keywords
Analytic number theory
;
L functions
;
automorphic forms
;
the Delta method
;
subconvexity
;
Quantum Unique Ergodicity
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Leung, W. H. (2022).
A Reformulation of the Delta Method and the Subconvexity Problem
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1650554459410968
APA Style (7th edition)
Leung, Wing Hong.
A Reformulation of the Delta Method and the Subconvexity Problem.
2022. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1650554459410968.
MLA Style (8th edition)
Leung, Wing Hong. "A Reformulation of the Delta Method and the Subconvexity Problem." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1650554459410968
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
osu1650554459410968
Download Count:
424
Copyright Info
© 2022, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.