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Thesis.pdf (2.43 MB)
ETD Abstract Container
Abstract Header
Spherical and Spheroidal Harmonics: Examples and Computations
Author Info
Zhao, Lin
ORCID® Identifier
http://orcid.org/0000-0002-1078-887X
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1512004235488354
Abstract Details
Year and Degree
2017, Master of Science, Ohio State University, Mathematics.
Abstract
This thesis introduces the theory of spherical and spheroidal harmonics, with emphasis on algorithms, computations, and explicit examples. In particular, we collect in one place several viewpoints on spherical and spheroidal harmonics, and clarify how the various viewpoints are related and how to transition between them. The ultimate goal is to be able to apply the spheroidal harmonics in calculating the spacing distributions of eigenvalues of the Gaussian unitary ensemble (GUE) random matrices. These eigenvalue statistics are conjectured to model corresponding statistics for zeros of the Riemann zeta function. New results are presented for comparing statistics of zeros and eigenvalues.
Committee
Ghaith Hiary (Advisor)
Roman Holowinsky (Committee Member)
Pages
98 p.
Subject Headings
Mathematics
Keywords
spherical harmonics
;
spheroidal harmonics
;
Riemann zeta zero
;
Gaussian unitary ensemble
;
spacing distributions
;
Riemann hypothesis
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Citations
Zhao, L. (2017).
Spherical and Spheroidal Harmonics: Examples and Computations
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512004235488354
APA Style (7th edition)
Zhao, Lin.
Spherical and Spheroidal Harmonics: Examples and Computations.
2017. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1512004235488354.
MLA Style (8th edition)
Zhao, Lin. "Spherical and Spheroidal Harmonics: Examples and Computations." Master's thesis, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512004235488354
Chicago Manual of Style (17th edition)
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Document number:
osu1512004235488354
Download Count:
3,989
Copyright Info
© 2017, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.