Zeros of Certain Combinations of Products of Eisenstein Series

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/44558k642

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Attribute Name	Values
Creator	Klangwang, Jetjaroen
Abstract	In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower boundary arc of the fundamental domain. Then, we introduce families of certain combinations of products of Eisenstein series and explore the location of their zeros in the fundamental domain. By extending F.K.C. Rankin and Swinnerton-Dyer argument, we show that almost all modular forms in our families have property that many of their zeros in the fundamental domain lie on the boundary of the fundamental domain.
License	All rights reserved
Resource Type	Dissertation
Date Issued	2018-05-30
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2018
Advisor	Swisher, Holly M.
Committee Member	Guo, Ren Petsche, Clayton Flahive, Mary E.
Academic Affiliation	Mathematics
Subject	Automorphic forms Number theory Elliptic functions
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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