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Test Vectors of Rankin-Selberg Convolutions for General Linear Groups
Kim, Kyung-Mi

2010, Doctor of Philosophy, Ohio State University, Mathematics.
In the integral representation of the local Rankin-Selberg
L-function of a pair
(π1,π2) for
GLn(F)
× GLm(F) with n
m over a non-archimedian field F,
we know that L(s,π1×
π2) is a finite sum
I(s,Wπ1,i,
Wπ2,i) (or
I(s,
Wπ1,i, Wπ2,i,
Φi) for n=m) of local
integrals, where
(Wπ1,i,
Wπ2,i) or
(Wπ1,i,
Wπ2,i,
Φi)
are test vectors of the
pair (π1, π2). Our goal is to find explicit formulas
for test vectors for any pair (π1, π2) with π1
in Irr(GL(n)) and π2Irr(GL(m)). In this dissertation, we
prove that one local integral
computes L(s,π1×
π2) for any unramified π2.
We construct a test vector
of any pair (π1,π2) for
GL(n) × GL(1). We
also show that most pairs (π1× π2) 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.
Dr. James Cogdell (Advisor)
Dr. Wenzhi Luo (Committee Member)
Dr. Warren Sinnott (Committee Member)
125 p.

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Kim, K. (2010). Test Vectors of Rankin-Selberg Convolutions for General Linear Groups. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Kim, Kyung-Mi. "Test Vectors of Rankin-Selberg Convolutions for General Linear Groups." Electronic Thesis or Dissertation. Ohio State University, 2010. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Kim, Kyung-Mi "Test Vectors of Rankin-Selberg Convolutions for General Linear Groups." Electronic Thesis or Dissertation. Ohio State University, 2010. https://etd.ohiolink.edu/

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