BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Abhishek Saha (Queen Mary University of London) DTSTART:20200508T110000Z DTEND:20200508T120000Z DTSTAMP:20260423T021236Z UID:NTdL/2 DESCRIPTION:Title: Cri tical L-values and congruence primes for Siegel modular forms\nby Abhi shek Saha (Queen Mary University of London) as part of Number theory durin g lockdown\n\n\nAbstract\nI will explain some recent joint work with Pital e and\nSchmidt where we obtain an explicit integral representation for the \ntwisted standard L-function on GSp_{2n} \\times GL_1 associated to a\nho lomorphic vector-valued Siegel cusp form of degree n and arbitrary\nlevel\ , and a Dirichlet character. By combining this integral\nrepresentation wi th a detailed arithmetic study of nearly holomorphic\nSiegel cusp forms (j oint with Pitale\, Schmidt\, and Horinaga) we are\nable to prove an algebr aicity result for the critical L-values on\nGSp_{2n} \\times GL_1. To ref ine this result further\, we prove that the\npullback of the nearly holomo rphic Eisenstein series that appears in\nour integral representation is ac tually cuspidal in each variable and\nhas nice p-adic arithmetic propertie s. This directly leads to a result\non congruences between Hecke eigenvalu es of two Siegel cusp forms of\ndegree 2 modulo primes dividing a certain quotient of L-values.\nFinally\, I will describe a second\, more refined v ersion of our\ncongruence theorem\, that is obtained by looking at Arthur packets and\nthe refined Gan-Gross-Prasad conjecture in this particular se tup.\n LOCATION:https://researchseminars.org/talk/NTdL/2/ END:VEVENT END:VCALENDAR