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Thesis_Yan.pdf (547.25 KB)
ETD Abstract Container
Abstract Header
L-function for Sp(4)xGL(2) via a non-unique model
Author Info
Yan, Pan
ORCID® Identifier
http://orcid.org/0000-0002-9497-4046
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1650033008566954
Abstract Details
Year and Degree
2022, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
We prove a conjecture of Ginzburg and Soudry on an integral representation for the tensor product partial L-function attached to a pair of irreducible automorphic cuspidal representations of Sp_4(A) and GL_2(A), which is derived from the twisted doubling method of Cai, Friedberg, Ginzburg and Kaplan. We show that the integral unfolds to a non-unique model and analyze it using the New Way method of Piatetski-Shapiro and Rallis. As applications, we determine the poles of the tensor product partial L-function and relate the existence of the poles to the non-vanishing of certain period integrals. Moreover, for certain family of cuspidal representations of GL_2(A), we prove that the tensor product partial L-function is holomorphic.
Committee
James Cogdell (Advisor)
Wenzhi Luo (Committee Member)
Roman Holowinsky (Committee Member)
Pages
105 p.
Subject Headings
Mathematics
Keywords
New Way method
;
non-unique model
;
twisted doubling integrals
;
Casselman-Shalika-Speh representations
;
periods
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Citations
Yan, P. (2022).
L-function for Sp(4)xGL(2) via a non-unique model
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1650033008566954
APA Style (7th edition)
Yan, Pan.
L-function for Sp(4)xGL(2) via a non-unique model.
2022. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1650033008566954.
MLA Style (8th edition)
Yan, Pan. "L-function for Sp(4)xGL(2) via a non-unique model." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1650033008566954
Chicago Manual of Style (17th edition)
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Document number:
osu1650033008566954
Download Count:
166
Copyright Info
© 2022, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.