BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vesselin Dimitrov (Toronto) DTSTART:20200612T150000Z DTEND:20200612T160000Z DTSTAMP:20260418T063754Z UID:LNTS/8 DESCRIPTION:Title: p-a dic Eisenstein series\, arithmetic holonomicity criteria\, and irrationali ty of the 2-adic $\\zeta(5)$\nby Vesselin Dimitrov (Toronto) as part o f London number theory seminar\n\n\nAbstract\nIn this exposition of a join t work in progress with Frank Calegari and Yunqing Tang\, I will explain a new arithmetic criterion for a formal function to be holonomic\, and how it revives an approach to the arithmetic nature of special values of L-fun ctions. The new consequence to be proved in this talk is the irrationality of the 2-adic version of $\\zeta(5)$ (of Kubota-Leopoldt). But I will als o draw a parallel to a work of Zudilin\, and try to leave some additional open ends where the holonomicity theorem could be useful. The ingredients of the irrationality proof are Calegari's p-adic counterpart of the Apery- Beukers method\, which is based on the theory of overconvergent p-adic mod ular forms (IMRN\, 2005) taking its key input from Buzzard's theorem on p- adic analytic continuation (JAMS\, 2002)\, and a Diophantine approximation method of Andre enhanced to a power of the modular curve $X_0(2)$. The ov erall argument\, as we shall discuss\, turns out to bear a surprising affi nity to a recent solution of the Schinzel-Zassenhaus conjecture on the orb its of Galois around the unit circle.\n LOCATION:https://researchseminars.org/talk/LNTS/8/ END:VEVENT END:VCALENDAR