Staff profile

• Automorphic forms
• Number Theory

• 2012: Editor of the Abhandlungen Math. Seminar Hamburg (2012-present):

Chapter in book

• Spectacle cycles with coefficients and modular forms of half-integral weight
  
  Funke, J., & Millson, J. (2011). Spectacle cycles with coefficients and modular forms of half-integral weight. In J. Cogdell, J. Funke, M. Rapoport, & T. Yang (Eds.), Arithmetic geometry and automorphic forms. (pp. 91-154). International Press.
• On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
  
  Bruinier, J., & Funke, J. (2010). On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift. In J. Lepowsky, J. McKay, & M. Tuite (Eds.), Moonshine : the first quarter century and beyond : proceedings of a workshop on the moonshine conjectures and vertex algebras. (pp. 12-39). Cambridge University Press. https://doi.org/10.1017/cbo9780511730054.004

Conference Paper

• Special cohomology classes for the Weil representation
  
  Funke, J. (2008, October 1). Special cohomology classes for the Weil representation. Presented at Automorphic Representations, Automorphic Forms, L-functions, and Related Topics, Kyoto.
• CM points and weight 3/2 modular forms
  
  Funke, J. (2007). CM points and weight 3/2 modular forms. In W. Duke & Y. Tschinkel (Eds.), Analytic number theory : a tribute to Gauss and Dirichlet. (pp. 107-127). American Mathematical Society.

Edited book

• Arithmetic Geometry and Automorphic forms, Volume in honor of the 60th birthday of Stephen S. Kudla.
  
  Funke, J., Cogdell, J., Rapoprt, M., & Yang, T. (Eds.). (2011). Arithmetic Geometry and Automorphic forms, Volume in honor of the 60th birthday of Stephen S. Kudla. International Press and the Higher Education Press of China.

Journal Article

• On Jacobi–Weierstrass mock modular forms
  
  Alfes, C., Funke, J., Mertens, M. H., & Rosu, E. (2025). On Jacobi–Weierstrass mock modular forms. Advances in Mathematics, 465, Article 110147. https://doi.org/10.1016/j.aim.2025.110147
• The Shimura-Shintani correspondence via singular theta lifts and currents
  
  Crawford, J., & Funke, J. (2023). The Shimura-Shintani correspondence via singular theta lifts and currents. International Journal of Number Theory, 19(10). https://doi.org/10.1142/s1793042123501178
• Indefinite theta series: the case of an N-gon
  
  Funke, J., & Kudla, S. (2023). Indefinite theta series: the case of an N-gon. Pure and Applied Mathematics Quarterly, 19 (2023)(1), 191-231. https://doi.org/10.4310/pamq.2023.v19.n1.a8
• The construction of Green currents and singular theta lifts for unitary groups
  
  Funke, J., & Hofmann, E. (2021). The construction of Green currents and singular theta lifts for unitary groups. Transactions of the American Mathematical Society, 374(4), 2909-2947. https://doi.org/10.1090/tran/8289
• On some incomplete theta integrals
  
  Funke, J., & Kudla, S. (2019). On some incomplete theta integrals. Compositio Mathematica, 155(9), 1711-1746. https://doi.org/10.1112/s0010437x19007504
• Modularity of generating series of winding numbers
  
  Bruinier, J., Funke, J., Imamoḡlu, Ö, & Li, Y. (2018). Modularity of generating series of winding numbers. Research in the Mathematical Sciences, 5(2), Article 23. https://doi.org/10.1007/s40687-018-0140-6
• Degenerate Whittaker functions for Sp_n(R)
  
  Bruinier, J., Funke, J., & Kudla, S. (2018). Degenerate Whittaker functions for Sp_n(R). International Mathematics Research Notices, 2018(1), 1-56. https://doi.org/10.1093/imrn/rnw218
• Mock modular forms and geometric theta functions for indefinite quadratic forms
  
  Funke, J., & Kudla, S. S. (2017). Mock modular forms and geometric theta functions for indefinite quadratic forms. Journal of Physics A: Mathematical and Theoretical, 50(40), Article 404001. https://doi.org/10.1088/1751-8121/aa848b
• Regularized theta liftings and periods of modular functions
  
  Bruinier, J., Funke, J., & Imamoglu, O. (2015). Regularized theta liftings and periods of modular functions. Journal für Die Reine Und Angewandte Mathematik, 2015(703), 43-93. https://doi.org/10.1515/crelle-2013-0035
• The geometric theta correspondence for Hilbert modular surfaces
  
  Funke, J., & Millson, J. (2014). The geometric theta correspondence for Hilbert modular surfaces. Duke Mathematical Journal, 163(1), 65-116. https://doi.org/10.1215/00127094-2405279
• Boundary behaviour of special cohomology classes arising from the Weil representation
  
  Funke, J., & Millson, J. (2013). Boundary behaviour of special cohomology classes arising from the Weil representation. Journal of the Institute of Mathematics of Jussieu, 12(3), 571-634. https://doi.org/10.1017/s1474748012000795
• Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms
  
  Funke, J., & Millson, J. (2006). Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms. American Journal of Mathematics, 128(4), 899-948. https://doi.org/10.1353/ajm.2006.0032
• Traces of CM values of modular functions
  
  Bruinier, J., & Funke, J. (2006). Traces of CM values of modular functions. Journal für Die Reine Und Angewandte Mathematik, 594, 1-33. https://doi.org/10.1515/crelle.2006.034
• On two geometric theta lifts
  
  Bruinier, J., & Funke, J. (2004). On two geometric theta lifts. Duke Mathematical Journal, 125(1), 45-90. https://doi.org/10.1215/s0012-7094-04-12513-8
• Heegner divisors and non-holomorphic modular forms
  
  Funke, J. (2002). Heegner divisors and non-holomorphic modular forms. Compositio Mathematica, 133(3), 289-321. https://doi.org/10.1023/a%3A1020002121978
• Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms
  
  Funke, J., & Millson, J. (2002). Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms. Manuscripta Mathematica, 107(4), 409-449. https://doi.org/10.1007/s002290100241
• Trace operator and theta series
  
  Böcherer, S., Funke, J., & Schulze-Pillot, J. (1999). Trace operator and theta series. Journal of Number Theory, 78(1), 119-139. https://doi.org/10.1006/jnth.1999.2404