BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Zahi Hazan (Tel Aviv Univ.) DTSTART:20220125T210000Z DTEND:20220125T220000Z DTSTAMP:20260423T005853Z UID:UAANTS/36 DESCRIPTION:Title: An Identity Relating Eisenstein Series on General Linear Groups\nby Za hi Hazan (Tel Aviv Univ.) as part of University of Arizona Algebra and Num ber Theory Seminar\n\n\nAbstract\nEisenstein 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 decomposit ion of the $L^2$-space of automorphic forms. In recent years\, new constru ctions of global integrals generating identities relating Eisenstein serie s were discovered. In 2018 Ginzburg and Soudry introduced two general iden tities relating Eisenstein series on split classical groups (generalizing Mœglin 1997\, Ginzburg-Piatetski-Shapiro-Rallis 1997\, and Cai-Friedberg- Ginzburg-Kaplan 2016)\, as well as double covers of symplectic groups (gen eralizing Ikeda 1994\, and Ginzburg-Rallis-Soudry 2011).\n\nWe consider th e Kronecker product embedding of two general linear 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 construction\, w e use a degenerate Eisenstein series of $\\mathrm{GL}{mn}(\\mathbb{A})$ as a kernel function on $\\mathrm{GL}{m}(\\mathbb{A}) \\otimes \\mathrm{GL}{ n}(\\mathbb{A})$. Integrating it against a cusp form on $\\mathrm{GL}{n}(\ \mathbb{A})$\, we obtain a 'semi-degenerate' Eisenstein series on $\\mathr m{GL}{m}(\\mathbb{A})$. Locally\, we find an interesting relation to the l ocal Godement-Jacquet integral.\n\nThis construction demonstrates the rise of interesting $L$-functions from integrals of doubling type\, as suggest ed by the philosophy of Ginzburg and Soudry.\n LOCATION:https://researchseminars.org/talk/UAANTS/36/ END:VEVENT END:VCALENDAR