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SUMMARY:Jeanine Van Order (Universität Bielefeld)
DTSTART:20201222T084000Z
DTEND:20201222T091000Z
DTSTAMP:20260423T010920Z
UID:JENTE/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/22/">F
 rom bounds for Fourier coefficients to bounds for Mordell-Weil ranks (and 
 beyond)</a>\nby Jeanine Van Order (Universität Bielefeld) as part of Japa
 n Europe Number Theory Exchange Seminar\n\n\nAbstract\nMotivated the by th
 e conjecture of Birch and Swinnerton-Dyer\, I will explain how the spectra
 l theory of automorphic forms on GL_2 and its two-fold metaplectic cover c
 an be used to derive unconditional bounds for Mordell-Weil ranks of ellipt
 ic curves in certain abelian towers of number fields. The surjectivity of 
 the archimedean local Kirillov map (or its classical manifestation in term
 s of Maass weight raising operators) plays a starring role here\, allowing
  one to realize the implicit L-values in terms as Fourier-Whittaker coeffi
 cients of distinct automorphic forms. This leads to both new progress and 
 open questions\, which I will also describe.\n
LOCATION:https://researchseminars.org/talk/JENTE/22/
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