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SUMMARY:Ulf Kühn (Universität Hamburg)
DTSTART:20211116T080000Z
DTEND:20211116T090000Z
DTSTAMP:20260423T010921Z
UID:JENTE/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/53/">R
 ealizations of the formal double Eisenstein space</a>\nby Ulf Kühn (Unive
 rsität Hamburg) as part of Japan Europe Number Theory Exchange Seminar\n\
 n\nAbstract\nIn this talk\, we introduce the formal double Eisenstein spac
 e $\\mathcal{E}_k$\, which is a generalization of the formal double zeta s
 pace $\\mathcal{D}_k$ of Gangl-Kaneko-Zagier. We show that $\\mathbb{Q}$-l
 inear from $\\mathcal{E}_k$ to $A$\, for some $\\mathbb{Q}$-algebra $A$\, 
 can be constructed from formal Laurent series that satisfy the Fay identit
 y. As the prototypical example\, we define the Kronecker realization\, whi
 ch lifts Gangl-Kaneko-Zagier's Bernoulli realization\, and whose image con
 sists of quasimodular forms for the full modular group. As an application 
 to the theory of modular forms\, we obtain a purely combinatorial proof of
  Ramanujan's differential equations for classical Eisenstein series. This 
 talk is based on a joint work with H. Bachmann and N. Matthes.\n
LOCATION:https://researchseminars.org/talk/JENTE/53/
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