Jens Funke, PhD University of Maryland College Park

Personal web page

Contact Jens Funke (email at jens.funke@durham.ac.uk)

Research Groups

Department of Mathematical Sciences

• Pure Mathematics
• Pure Mathematics: Algebra & Number Theory

Research Interests

• Automorphic forms
• Number Theory

Publications

Edited book

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

Chapter in book

• Funke, J. & Millson, J. (2011). Spectacle cycles with coefficients and modular forms of half-integral weight. In Arithmetic Geometry and Automorphic forms. Cogdell, J., Funke, J., Rapoport, M. & Yang, T. International Press and Higher Education Press, Beijing, China. 19: 91-154.
• Bruinier, J. & Funke, J. (2010). On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift. In Moonshine - the first quarter century and beyond: proceedings of a workshop on the moonshine conjectures and vertex algebras. Lepowsky, J., McKay, J. & Tuite, M. Cambridge Cambridge University Press. 12-39.

Journal Article

• Funke, Jens & Hofmann, Eric (Accepted). The construction of Green currents and singular theta lifts for unitary groups. Transactions of the American Mathematical Society
• Funke, Jens & Kudla, Stephen (2019). On some incomplete theta integrals. Compositio Mathematica 155(9): 1711-1746.
• Bruinier, J., Funke, J. & Kudla, S. (2018). Degenerate Whittaker functions for Sp_n(R). International Mathematics Research Notices 2018(1): 1-56.
• Bruinier, J., Funke, J., Imamoḡlu, Ö. & Li, Y. (2018). Modularity of generating series of winding numbers. Research in the Mathematical Sciences 5(2): 23.
• Funke, Jens & Kudla, Stephen S. (2017). Mock modular forms and geometric theta functions for indefinite quadratic forms. Journal of Physics A: Mathematical and Theoretical 50(40): 404001.
• Bruinier, Jan, Funke, Jens & Imamoglu, Ozlem (2015). Regularized theta liftings and periods of modular functions. Journal für die Reine und Angewandte Mathematik 2015(703): 43-93.
• Funke, Jens & Millson, John (2014). The geometric theta correspondence for Hilbert modular surfaces. Duke Mathematical Journal 163(1): 65-116.
• Funke, Jens & Millson, John (2013). Boundary behaviour of special cohomology classes arising from the Weil representation. Journal of the Institute of Mathematics of Jussieu 12(3): 571-634.
• 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.
• Bruinier, J. & Funke, J. (2006). Traces of CM values of modular functions. Journal fur die reine und angewandte Mathematik 594: 1-33.
• Bruinier, J. & Funke, J. (2004). On two geometric theta lifts. Duke Mathematical Journal 125(1): 45-90.
• 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.
• Funke, J. (2002). Heegner divisors and non-holomorphic modular forms. Compositio Mathematica 133(3): 289-321.
• Böcherer, S., Funke, J. & Schulze-Pillot, J. (1999). Trace operator and theta series. Journal of Number Theory 78(1): 119-139.

Conference Paper

• Funke, J. (2008), Special cohomology classes for the Weil representation, 1617: Automorphic Representations, Automorphic Forms, L-functions, and Related Topics. Kyoto, RIMS Kokyuroku, Kyoto, 106-119.
• Funke, J. (2007), CM points and weight 3/2 modular forms, in Duke, W. & Tschinkel, Y. eds, Clay Mathematics Proceedings 7: Analytic Number Theory: A Tribute to Gauss and Dirichlet. Göttingen, Germany, American Mathematical Society, Göttingen, 107-127.