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SUMMARY:Non-vanishing of finite order twists of L-values via horizontal p-
 adic L-functions
DTSTART:20231102T141500
DTEND:20231102T160000
DTSTAMP:20260924T105516Z
UID:86b01e50d225e445aa30558cbaba7ba1cc0eac202313cca450f0f3b7
CATEGORIES:Conferences - Seminars
DESCRIPTION:Asbjorn Nordentoft (Paris 13\nGoldfeld’s Conjecture predicts
  that exactly 50% of quadratic twists of a fixed elliptic curve have L-fun
 ction non-vanishing at the central point. Correspondingly\, when consideri
 ng twists by higher order Dirichlet characters\, it has been predicted by 
 David-Fearnly-Kisilevsky that 100% should be non-vanishing. Very little wa
 s previously known beyond the quadratic case as the problem lies beyond th
 e current technology of e.g. analytic number theory. In this talk I will p
 resent a p-adic approach relying on the construction of ‘horizontal p-ad
 ic L-functions’. This yields strong quantitative non-vanishing results f
 or general order twists. In particular\, we obtain the best result towards
  Goldfeld's Conjecture for one hundred percent of elliptic curves (improvi
 ng on a result of Ono). I will also present applications to simultaneous n
 on-vanishing and Diophantine stability.\nThis talk is based on joint work 
 with Daniel Kriz.\nIn the introductory talk\, I will give an introduction 
 to the concept in arithmetic statistics known as 'Diophantine stability' a
 nd the connections to the Birch—Swinnerton-Dyer Conjecture. In particula
 r\, I will discuss Goldfeld's Conjecture\, as well as the case of the cycl
 otomic $p$-tower studied in Iwasawa theory.  \n 
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012
STATUS:CONFIRMED
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