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Residues of Certain Eisenstein Serie...

An, Shengmei,

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Residues of Certain Eisenstein Series of Classical Groups and the First Term Identities /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Residues of Certain Eisenstein Series of Classical Groups and the First Term Identities // Shengmei An.
Author:	An, Shengmei,
Description:	1 electronic resource (87 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-08, Section: B.
Contained By:	Dissertations Abstracts International85-08B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30991078
ISBN:	9798381723038

Residues of Certain Eisenstein Series of Classical Groups and the First Term Identities /
An, Shengmei,

Residues of Certain Eisenstein Series of Classical Groups and the First Term Identities /Shengmei An. - 1 electronic resource (87 pages)

Source: Dissertations Abstracts International, Volume: 85-08, Section: B.

In this thesis, we are going to study certain degenerate Eisenstein series for the Symplectic groups and Orthogonal groups. We are going to prove the analytical properties, particularly the pole locations and exact order, as well as the first term identity.In order to understand the pole information, we first compute the normalizing factor for the Eisenstein series using the Gindikin-Karpalevich formula. Then we get a recursion formula with normalized sections to connect the Eisenstein series for Sp2n (or O2n) with Sp2(n−1) (or O2(n−1), correspondingly) by unfolding the Eisenstein series. From the recursion formula, we can get the range for pole locations for the Eisenstein series. The recursion formula also leads to a functional equation that demonstrates a symmetry between two Eisenstein series at different points. By using this functional equation as well as the recursion formula, we can get the exact pole order as well as the first term identity for spherical sections.

English

ISBN: 9798381723038Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Analytical properties

Residues of Certain Eisenstein Series of Classical Groups and the First Term Identities /
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245 1 0 $a Residues of Certain Eisenstein Series of Classical Groups and the First Term Identities / $c Shengmei An.
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300 $a 1 electronic resource (87 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 85-08, Section: B.
500 $a Advisors: Jiang, Dihua.
502 $b Ph.D. $c University of Minnesota $d 2024.
520 $a In this thesis, we are going to study certain degenerate Eisenstein series for the Symplectic groups and Orthogonal groups. We are going to prove the analytical properties, particularly the pole locations and exact order, as well as the first term identity.In order to understand the pole information, we first compute the normalizing factor for the Eisenstein series using the Gindikin-Karpalevich formula. Then we get a recursion formula with normalized sections to connect the Eisenstein series for Sp2n (or O2n) with Sp2(n−1) (or O2(n−1), correspondingly) by unfolding the Eisenstein series. From the recursion formula, we can get the range for pole locations for the Eisenstein series. The recursion formula also leads to a functional equation that demonstrates a symmetry between two Eisenstein series at different points. By using this functional equation as well as the recursion formula, we can get the exact pole order as well as the first term identity for spherical sections.
546 $a English
590 $a School code: 0130
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical physics. $3 2144760
653 $a Analytical properties
653 $a Orthogonal groups
653 $a Recursion formula
653 $a Eisenstein series
690 $a 0405
690 $a 0642
690 $a 0753
690 $a 0364
710 2 $a University of Minnesota. $b Mathematics. $e degree granting institution. $3 3820893
720 1 $a Jiang, Dihua $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 85-08B.
790 $a 0130
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30991078