Identities of cycle integrals of weak Maass forms

  • Claudia Alfes-NeumannEmail author
  • Markus Schwagenscheidt


We prove identities between cycle integrals of non-holomorphic modular forms arising from applications of various differential operators to weak Maass forms


Weak Maass forms Geodesic cycle integrals 

Mathematics Subject Classification

11F11 11F25 11F67 



We thank the anonymous referee for helpful suggestions.


  1. 1.
    Bringmann, K., Guerzhoy, P., Kane, B.: Shintani lifts and fractional derivatives for harmonic weak Maass forms. Adv. Math. 255, 641–671 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bringmann, K., Guerzhoy, P., Kane, B.: On cycle integrals of weakly holomorphic modular forms. Math. Proc. Camb. Philos. Soc. 158(3), 439–449 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bruinier, J.H., Funke, J.: On two geometric theta lifts. Duke Math. J. 125(1), 45–90 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bruinier, J.H., Ono, K., Rhoades, R.C.: Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues. Math. Ann. 342(3), 673–693 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kohnen, W., Zagier, D.: Modular forms with rational periods. In: Rankin, R.A. (ed.) Modular Forms, pp. 197–249. Ellis Horwood, Chicheseter (1985)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematical InstitutePaderborn UniversityPaderbornGermany
  2. 2.Mathematical InstituteUniversity of CologneCologneGermany

Personalised recommendations