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osu1279896776.pdf (659.08 KB)
ETD Abstract Container
Abstract Header
Test Vectors of Rankin-Selberg Convolutions for General Linear Groups
Author Info
Kim, Kyung-Mi
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1279896776
Abstract Details
Year and Degree
2010, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
In the integral representation of the local Rankin-Selberg
L
-function of a pair (
π
1
,
π
2
) for
GL
n
(
F
) ×
GL
m
(
F
) with
n
≥
m
over a non-archimedian field
F
, we know that
L
(
s
,
π
1
×
π
2
) is a finite sum ∑
I
(
s
,
W
π
1
,
i
,
W
π
2
,
i
) (or ∑
I
(
s
,
W
π
1
,
i
,
W
π
2
,
i
, Φ
i
) for
n
=
m
) of local integrals, where (
W
π
1
,
i
,
W
π
2
,
i
) or (
W
π
1
,
i
,
W
π
2
,
i
, Φ
i
) are test vectors of the pair (
π
1
,
π
2
). Our goal is to find explicit formulas for test vectors for any pair (
π
1
,
π
2
) with
π
1
in
Irr
(
GL
(
n
)) and
π
2
∈
Irr
(
GL
(
m
)). In this dissertation, we prove that one local integral computes
L
(
s
,
π
1
×
π
2
) for any unramified
π
2
. We construct a test vector of any pair (
π
1
,
π
2
) for
GL
(
n
) ×
GL
(1). We also show that most pairs (
π
1
×
π
2
) for
GL
(
n
) ×
GL
(2) need at most two test vectors. As a generalization, we prove some pairs for
GL
(
n
) ×
GL
(
m
) are optimal 1-regular.
Committee
Dr. James Cogdell (Advisor)
Dr. Wenzhi Luo (Committee Member)
Dr. Warren Sinnott (Committee Member)
Pages
125 p.
Subject Headings
Mathematics
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Kim, K.-M. (2010).
Test Vectors of Rankin-Selberg Convolutions for General Linear Groups
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1279896776
APA Style (7th edition)
Kim, Kyung-Mi.
Test Vectors of Rankin-Selberg Convolutions for General Linear Groups.
2010. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1279896776.
MLA Style (8th edition)
Kim, Kyung-Mi. "Test Vectors of Rankin-Selberg Convolutions for General Linear Groups." Doctoral dissertation, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1279896776
Chicago Manual of Style (17th edition)
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Document number:
osu1279896776
Download Count:
1,337
Copyright Info
© 2010, some rights reserved.
Test Vectors of Rankin-Selberg Convolutions for General Linear Groups by Kyung-Mi Kim is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.