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SUMMARY:Jan-Willem van Ittersum (Utrecht University)
DTSTART:20201103T080000Z
DTEND:20201103T083000Z
DTSTAMP:20260423T010810Z
UID:JENTE/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/7/">A 
 Kaneko-Zagier equation for Jacobi forms</a>\nby Jan-Willem van Ittersum (U
 trecht University) as part of Japan Europe Number Theory Exchange Seminar\
 n\n\nAbstract\nThe Kaneko-Zagier equation is a second order differential e
 quation depending on a parameter k which gives rise to an infinite family 
 of modular forms as solutions. These solutions are closely related to Weie
 rstrass p function\, which becomes clear by considering the inverse (under
  composition) of a suitably normalized generating series of the solutions 
 for integer values of k. In this talk\, we study an analogue of the Kaneko
 -Zagier differential equation for Jacobi forms. We point to three features
  of the infinite family of solutions. First of all\, the solutions are qua
 si-Jacobi forms\, and we determine their transformation under the Jacobi g
 roup. Secondly\, the inverse of a suitable normalized generating series of
  these solutions is again a well-known function\, namely a ratio of theta 
 functions. Finally\, a special feature of the solutions is the polynomial 
 dependence of the index parameter. (Joint with Georg Oberdieck and Aaron P
 ixton)\n
LOCATION:https://researchseminars.org/talk/JENTE/7/
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