[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (10/03/2016, Tatiana Hessami Pilehrood, Vinayak Vatsal)
Guillermo Martinez-Zalce
martinez at crm.umontreal.ca
Wed Mar 9 09:28:53 EST 2016
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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY
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DATE :
Le jeudi 10 mars 2016 / Thursday, March 10, 2016
HEURE / TIME :
10 h 30 - 12 h / 10:30 a.m. - 12:00 p.m.
CONFERENCIER(S) / SPEAKER(S) :
Tatiana Hessami Pilehrood (University of Toronto)
TITRE / TITLE :
On duality relations between multiple zeta star values and Euler sums.
LIEU / PLACE :
McGill University, Burnside Hall salle BH920
RESUME / ABSTRACT :
In recent years, there has been intensive research on the Q-linear relations between multiple zeta (star) values. In this talk, we will discuss many families of identities for multiple zeta (star) values and their q-analogs. The main result is the duality relations between multiple zeta star values and Euler sums, which are generalizations of the Two-one formula by Ohno and Zudilin and some multiple harmonic sum identities. Such duality relations lead to a proof of the conjecture by Ihara et al. that the Hoffman $\star$-elements $\zeta^{\star}(s_1,\dots,s_r)$ with $s_i\in\{2,3\}$ span the vector space generated by multiple zeta values over Q. Based on joint work with Khodabakhsh Hessami Pilehrood and Jianqiang Zhao.
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DATE :
Le jeudi 10 mars 2016 / Thursday, March 10, 2016
HEURE / TIME :
14 h - 15 h 30 / 2:00 p.m. - 3:30 p.m.
CONFERENCIER(S) / SPEAKER(S) :
Vinayak Vatsal (University of British Columbia)
TITRE / TITLE :
Lambda-adic Waldspurger Packets
LIEU / PLACE :
Concordia University, Library Building, 9th floor, Salle/Room 921-04
RESUME / ABSTRACT :
Wadspurger has shown that the genuine automorphic cuspidal representations of the metaplectic cover S of SL_2 are divided naturally into packets, and that thse packets are indexed by the cuspidal automorphic representations of PGL_2. We construct packets of Lambda-adic modular forms of half integral weight, indexed by Lambda-adic forms on PGL_2. The elements of the Lambda-adic packets are nonzero, but they have specializations that vanish, owing to a trivial zero phenomenon and the sign of a complex root number. This is in contrast to the usual trivial zero phenomenon which arises from the vanishing of a p-adic factor.
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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Andrew Granville (andrew at dms.umontreal.ca)
Dimitris Koukoulopoulos (koukoulo at dms.umontreal.ca)
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