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UID:8b38532804d3d824f8801e0d1a03c718
CATEGORIES:Number Theory Seminar
CREATED:20230130T150421
SUMMARY:Number Theory Seminar
LOCATION:Hill 525
DESCRIPTION:Title: An Identity Relating Eisenstein Series on General Linear Groups\nSpe
aker:Zahi Hazan (Tel-Aviv)\nAbstract:\n \nEisenstein series are key objects
in the theory of automorphic forms. They play an important role in the stu
dy of automorphic (L)-functions, and they figure out in the spectral decomp
osition of the (L^2)-space of automorphic forms. In recent years, new const
ructions of global integrals generating identities relating Eisenstein seri
es were discovered. In 2018 Ginzburg and Soudry introduced two general iden
tities relating Eisenstein series on split classical groups (generalizing M
œglin 1997, Ginzburg-Piatetski-Shapiro-Rallis 1997, and Cai-Friedberg-Ginzb
urg-Kaplan 2016), as well as double covers of symplectic groups (generalizi
ng Ikeda 1994, and Ginzburg-Rallis-Soudry 2011).We consider the Kronecker p
roduct embedding of two general linear groups, (mathrm{GL}{m}(mathbb{A})) a
nd (mathrm{GL}{n}(mathbb{A})), in (mathrm{GL}{mn}(mathbb{A})). Now, similar
ly to Ginzburg and Soudry's construction, we use a degenerate Eisenstein se
ries of (mathrm{GL}{mn}(mathbb{A})) as a kernel function on (mathrm{GL}{m}(
mathbb{A}) otimes mathrm{GL}{n}(mathbb{A})). Integrating it against a cusp
form on (mathrm{GL}{n}(mathbb{A})), we obtain a 'semi-degenerate' Eisenstei
n series on (mathrm{GL}{m}(mathbb{A})). Locally, we find an interesting rel
ation to the local Godement-Jacquet integral.\nThis construction demonstrat
es the rise of interesting (L)-functions from integrals of doubling type, a
s suggested by the philosophy of Ginzburg and Soudry.\n
X-ALT-DESC;FMTTYPE=text/html:Title: An Identity Relating Eisenstein Series on General Linear Groups<
/span>
Speaker
:Z
ahi Hazan (Tel-Aviv)
Eisenstein series are key objects in the theory of
automorphic forms. They play an important role in the study of automorphic
(L)-functions, and they figure out in the spectral decomposition of the (L^
2)-space of automorphic forms. In recent years, new constructions of global
integrals generating identities relating Eisenstein series were discovered
. In 2018 Ginzburg and Soudry introduced two general identities relating Ei
senstein series on split classical groups (generalizing Mœglin 1997, Ginzbu
rg-Piatetski-Shapiro-Rallis 1997, and Cai-Friedberg-Ginzburg-Kaplan 2016),
as well as double covers of symplectic groups (generalizing Ikeda 1994, and
Ginzburg-Rallis-Soudry 2011).
We consider the Kronecker product embedding of two general li
near groups, (mathrm{GL}{m}(mathbb{A})) and (mathrm{GL}{n}(mathbb{A})), in
(mathrm{GL}{mn}(mathbb{A})). Now, similarly to Ginzburg and Soudry's constr
uction, we use a degenerate Eisenstein series of (mathrm{GL}{mn}(mathbb{A})
) as a kernel function on (mathrm{GL}{m}(mathbb{A}) otimes mathrm{GL}{n}(ma
thbb{A})). Integrating it against a cusp form on (mathrm{GL}{n}(mathbb{A}))
, we obtain a 'semi-degenerate' Eisenstein series on (mathrm{GL}{m}(mathbb{
A})). Locally, we find an interesting relation to the local Godement-Jacque
t integral.
This constructi
on demonstrates the rise of interesting (L)-functions from integrals of dou
bling type, as suggested by the philosophy of Ginzburg and Soudry.
CONTACT:Zahi Hazan (Tel-Aviv)
DTSTAMP:20260829T194748
DTSTART;TZID=America/New_York:20230131T140000
DTEND;TZID=America/New_York:20230131T150000
SEQUENCE:0
TRANSP:OPAQUE
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