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SUMMARY:Wadim Zudilin (Radboud University Nijmegen)
DTSTART:20201013T083000Z
DTEND:20201013T090000Z
DTSTAMP:20260423T010810Z
UID:JENTE/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/2/">(Q
 uasi-)magnetic modular forms</a>\nby Wadim Zudilin (Radboud University Nij
 megen) as part of Japan Europe Number Theory Exchange Seminar\n\n\nAbstrac
 t\nGiven a positive even integer $k$\, let $E_k(\\tau)$ stands for the nor
 malised Eisenstein series of weight $k$\; denote $$\\Delta(\\tau)=q\\prod_
 {m=1}^\\infty(1-q^m)^{24}=(E_4^3-E_6^2)/1728$$ with $q=e^{2\\pi i\\tau}$\,
  and $\\delta=\\frac{1}{2\\pi i}\\frac{d}{\\d\\tau}=q\\frac{d}{dq}$. About
  ten years ago Honda and Kaneko observed surprising arithmetic properties 
 of the meromorphic modular function $\\Delta^{5/6}/E_4^2$ of weight 2\, wh
 ile the recent work of Li and Neururer (inspired by an observation of Broa
 dhurst and this speaker) brought to life an even stronger arithmetic for t
 he modular function $\\Delta/E_4^2$ of weight 4. To convince the attendee 
 about it\, you are invited to verify that the anti-derivatives $\\delta^{-
 1}(\\Delta/E_4^2)$ and $\\delta^{-1}(E_4\\Delta/E_6^2)$ have integer coeff
 icients in their $q$-expansions. At the same time\, these series are trans
 cendental over the field of quasi-modular functions. I will discuss this p
 henomenon (in a greater generality!) and ideas behind its proof in my talk
 . The talk is based on my joint work with Vicenţiu Paşol.\n
LOCATION:https://researchseminars.org/talk/JENTE/2/
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