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BEGIN:VEVENT
UID:8b38532804d3d824f8801e0d1a03c718
CATEGORIES:Number Theory Seminar
CREATED:20230130T150421
SUMMARY:Number Theory Seminar
LOCATION:Hill 525
DESCRIPTION:<div style="border: 0px; font-style: normal; font-weight: 400; font-size: 1
 5px; line-height: inherit; font-family: Calibri, Arial, Helvetica, sans-ser
 if; margin: 0px; padding: 0px; vertical-align: baseline; color: #242424; le
 tter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text
 -transform: none; white-space: normal; widows: 2; word-spacing: 0px; backgr
 ound-color: white;"><div style="border: 0px; font-style: inherit; font-vari
 ant: inherit; font-weight: inherit; font-size: 15px; line-height: inherit; 
 font-family: inherit; margin: 0px; padding: 0px; vertical-align: baseline; 
 color: #242424; background-color: white;"><div style="border: 0px; font: in
 herit; margin: 0px; padding: 0px; vertical-align: baseline; color: inherit;
 "><p class="elementToProof" style="font-size: 12pt; font-family: 'Times New
  Roman', serif; background-color: white; margin: 0px;"><span style="border:
  0px; font: inherit; margin: 0px; padding: 0px; vertical-align: baseline; c
 olor: inherit;"><strong><span class="ContentPasted0" style="border: 0px; fo
 nt-style: inherit; font-variant: inherit; font-weight: inherit; font-size: 
 12pt; line-height: inherit; font-family: Calibri, Helvetica, sans-serif; ma
 rgin: 0px; padding: 0px; vertical-align: baseline; color: black; background
 -color: white;">Title:&nbsp;</span><span class="ContentPasted0" style="bord
 er: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; 
 font-size: inherit; line-height: inherit; font-family: Calibri, Helvetica, 
 sans-serif; margin: 0px; padding: 0px; vertical-align: baseline; color: bla
 ck; background-color: white;"><span class="ContentPasted1" style="border: 0
 px; font-style: inherit; font-variant: inherit; font-weight: 400; font-size
 : 12pt; line-height: inherit; font-family: Calibri, sans-serif; margin: 0px
 ; padding: 0px; vertical-align: baseline; color: #242424; background-color:
  #ffffff;">An Identity Relating Eisenstein Series on General Linear Groups<
 /span></span><span style="border: 0px; font-style: inherit; font-variant: i
 nherit; font-weight: inherit; font-size: inherit; line-height: inherit; fon
 t-family: Calibri, sans-serif; margin: 0px; padding: 0px; vertical-align: b
 aseline; color: black; background-color: white;"><br class="ContentPasted0"
 ></span></strong></span></p></div><div style="border: 0px; font: inherit; m
 argin: 0px; padding: 0px; vertical-align: baseline; color: inherit;"><p cla
 ss="elementToProof" style="font-size: 12pt; font-family: 'Times New Roman',
  serif; background-color: white; margin: 0px;"><span style="border: 0px; fo
 nt: inherit; margin: 0px; padding: 0px; vertical-align: baseline; color: in
 herit;"><strong><span class="ContentPasted0" style="border: 0px; font-style
 : inherit; font-variant: inherit; font-weight: inherit; font-size: 12pt; li
 ne-height: inherit; font-family: Calibri, Helvetica, sans-serif; margin: 0p
 x; padding: 0px; vertical-align: baseline; color: black; background-color: 
 white;">Spe</span></strong></span><span style="border: 0px; font: inherit; 
 margin: 0px; padding: 0px; vertical-align: baseline; color: inherit;"><span
  style="border: 0px; font-style: inherit; font-variant: inherit; font-weigh
 t: inherit; font-size: inherit; line-height: inherit; font-family: Calibri,
  Helvetica, sans-serif; margin: 0px; padding: 0px; vertical-align: baseline
 ; color: black; background-color: white;"><span style="border: 0px; font-st
 yle: inherit; font-variant: inherit; font-weight: inherit; font-size: 12pt;
  line-height: inherit; font-family: inherit; margin: 0px; padding: 0px; ver
 tical-align: baseline; color: inherit;"><strong class="ContentPasted0">aker
 :</strong></span><span style="border: 0px; font: inherit; margin: 0px; padd
 ing: 0px; vertical-align: baseline; color: inherit;"><span class="ContentPa
 sted0" style="border: 0px; font-style: inherit; font-variant: inherit; font
 -weight: inherit; font-size: 12pt; line-height: inherit; font-family: inher
 it; margin: 0px; padding: 0px; vertical-align: baseline; color: inherit;">Z
 ahi Hazan (Tel-Aviv)</span></span></span></span></p></div><div style="borde
 r: 0px; font: inherit; margin: 0px; padding: 0px; vertical-align: baseline;
  color: inherit;"><p style="font-size: 12pt; font-family: 'Times New Roman'
 , serif; background-color: white; margin: 0px;"><span style="border: 0px; f
 ont: inherit; margin: 0px; padding: 0px; vertical-align: baseline; color: i
 nherit;"><strong><span class="ContentPasted0" style="border: 0px; font-styl
 e: inherit; font-variant: inherit; font-weight: inherit; font-size: 12pt; l
 ine-height: inherit; font-family: Calibri, Helvetica, sans-serif; margin: 0
 px; padding: 0px; vertical-align: baseline; color: black; background-color:
  white;">Abstract:</span><span style="border: 0px; font-style: inherit; fon
 t-variant: inherit; font-weight: inherit; font-size: inherit; line-height: 
 inherit; font-family: Calibri, sans-serif; margin: 0px; padding: 0px; verti
 cal-align: baseline; color: black; background-color: white;"><span style="b
 order: 0px; font-style: inherit; font-variant: inherit; font-weight: 400; f
 ont-size: 15px; line-height: inherit; font-family: inherit; margin: 0px; pa
 dding: 0px; vertical-align: baseline; color: #242424; background-color: whi
 te;"><span class="ContentPasted0" style="border: 0px; font-style: inherit; 
 font-variant: inherit; font-weight: inherit; font-size: 12pt; line-height: 
 inherit; font-family: Calibri, Helvetica, sans-serif; margin: 0px; padding:
  0px; vertical-align: baseline; color: inherit;"></span></span></span></str
 ong></span></p><p class="elementToProof" style="font-size: medium; margin-t
 op: 0px; margin-bottom: 0px; text-align: left;">&nbsp;</p></div></div></div
 ><p class="ContentPasted2" style="font-style: normal; font-weight: 400; let
 ter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-
 transform: none; white-space: normal; widows: 2; word-spacing: 0px; backgro
 und-color: #ffffff; color: #242424; font-size: 11pt; font-family: Calibri, 
 sans-serif; margin: 0px;"><span style="border: 0px; font-style: inherit; fo
 nt-variant: inherit; font-weight: inherit; font-size: 12pt; line-height: in
 herit; font-family: inherit; margin: 0px; padding: 0px; vertical-align: bas
 eline; color: inherit;">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).</span><br class="ContentPasted2"><br class="
 ContentPasted2"><span style="border: 0px; font-style: inherit; font-variant
 : inherit; font-weight: inherit; font-size: 12pt; line-height: inherit; fon
 t-family: inherit; margin: 0px; padding: 0px; vertical-align: baseline; col
 or: inherit;">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.</span></p><p class="ContentPasted2 elementToProof" style="font-
 style: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-a
 lign: start; text-indent: 0px; text-transform: none; white-space: normal; w
 idows: 2; word-spacing: 0px; background-color: #ffffff; color: #242424; fon
 t-size: 11pt; font-family: Calibri, sans-serif; margin: 0px;"><span style="
 border: 0px; font-style: inherit; font-variant: inherit; font-weight: inher
 it; font-size: 12pt; line-height: inherit; font-family: inherit; margin: 0p
 x; padding: 0px; vertical-align: baseline; color: inherit;">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.</span></
 p>
CONTACT:Zahi Hazan (Tel-Aviv)
DTSTAMP:20260829T215338
DTSTART;TZID=America/New_York:20230131T140000
DTEND;TZID=America/New_York:20230131T150000
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
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