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SUMMARY:Markus Schwagenscheidt (ETH Zürich)
DTSTART:20201110T080000Z
DTEND:20201110T083000Z
DTSTAMP:20260423T010809Z
UID:JENTE/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/9/">Ar
 ithmetic properties of meromorphic modular forms</a>\nby Markus Schwagensc
 heidt (ETH Zürich) as part of Japan Europe Number Theory Exchange Seminar
 \n\n\nAbstract\nWhile investigating the Doi-Naganuma lift\, Zagier studied
  certain cusp forms f_{k\,d} of weight 2k associated to positive discrimin
 ants d. These cusp forms also appear prominently in the kernel function fo
 r the Shimura-Shintani correspondence. Moreover\, Kohnen and Zagier showed
  that they have rational periods and geodesic cycle integrals. The natural
  generalization of the function f_{k\,d} to negative discriminants d yield
 s a meromorphic modular form with poles at the CM points of discriminant d
 . Together with C. Alfes-Neumann\, K. Bringmann\, S. Löbrich\, and J. Mal
 es\, we showed that these meromorphic modular forms have interesting arith
 metic properties\, too. Indeed\, they have rational periods and cycle inte
 grals\, and integral Fourier coefficients which satisfy strong divisibilit
 y conditions. Moreover\, their Fourier coefficients are non-vanishing and 
 have very regular sign changes. If time permits\, we will also discuss a s
 urprising relation with the coefficients of the modular j-invariant and th
 e partition function.\n
LOCATION:https://researchseminars.org/talk/JENTE/9/
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