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UID:6010@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220616T140000
DTEND;TZID=Europe/Paris:20220616T150000
DTSTAMP:20241120T200717Z
URL:https://www.i2m.univ-amu.fr/evenements/integral-representations-relate
 d-to-triple-product-l-functions/
SUMMARY:Jayce Getz (Duke university): Integral representations related to t
 riple product L-functions
DESCRIPTION:Jayce Getz: Triple product L-functions are the Langlands L-func
 tions attached to a triple of automorphic representations of GL_{r_i} for 
 positive integers r_1\,r_2\,r_3 and the tensor product representation GL_{
 r_1} \\times GL_{r_2} \\times GL_{r_3} \\lto \\GL_{r_1r_2r_3}.\nIf we knew
  their analytic properties then by the converse theorem one would be able 
 to deduce the automorphy of Rankin-Selberg products of automorphic represe
 ntations.  This corresponds to the special case r_3=1.   This in turn wo
 uld make huge inroads into Langlands functoriality.  I will report on joi
 nt work with Pam Gu\, Chun-Hsien Hsu\, and Spencer Leslie in which we cons
 truct an integral representation related to triple product L-functions\, g
 eneralizing work of Garrett\, Piatetski-Shapiro\, and Rallis in the case r
 _1=r_2=r_3=2.  I will also comment on the obstacles to using this integra
 l representation to obtain the functional equation of triple product L-fun
 ctions\, and how one might overcome them.\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/05/Jayce_Getz.png
CATEGORIES:Séminaire,Représentations des Groupes Réductifs
LOCATION:Luminy\, Campus des Sciences de Luminy\, Marseille\, 13009\, Franc
 e
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 ny\, Marseille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy:geo:0,0
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