BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Asbjørn Nordentoft (Université Paris-Saclay) DTSTART:20240228T160000Z DTEND:20240228T170000Z DTSTAMP:20260418T064247Z UID:LNTS/122 DESCRIPTION:Title: H orizontal p-adic L-functions\nby Asbjørn Nordentoft (Université Pari s-Saclay) as part of London number theory seminar\n\nLecture held in A1/3\ , Physics Building.\n\nAbstract\nGoldfeld’s Conjecture predicts that exa ctly 50% of quadratic twists of a fixed elliptic curve will have L-functio n vanishing at the central point. When considering the non-vanishing of tw ists of elliptic curve L-functions by characters of (fixed) order greater than 2\, it has been predicted by David-Fearnly-Kisilevsky that 100% shoul d be non-vanishing. Very little was previously known outside the quadratic case as the problem lies beyond the current technology of e.g. analytic n umber theory. In this talk I will present a p-adic approach relying on the construction of a ‘horizontal p-adic L-function’. This approach yield s strong quantitative non-vanishing results for general order twists. In p articular\, we obtain the best bound towards Goldfeld's Conjecture for one hundred percent of elliptic curves (improving on a result of Ono).\n\nThi s is joint work with Daniel Kriz.\n LOCATION:https://researchseminars.org/talk/LNTS/122/ END:VEVENT END:VCALENDAR