Jan Hendrik Bruinier

Research papers and preprints

• Intersections of special cycles on Shimura curves and Siegel Maass forms (with Y. Li and M. Möller), preprint (2026). pdf.
• Lefschetz decompositions of Kudla-Millson theta functions (with R. Zuffetti), preprint (2024). pdf.
• Modularity of special 0-cycles on toroidal compactifications of Shimura Varieties (with E. Rosu and S. Zemel), preprint (2024). pdf.
• Formal Siegel modular forms for arithmetic subgroups (with M. Raum), Transactions of the AMS, Ser. B 11 (2024), 1394-1434. pdf.
• Harmonic weak Maass forms and periods II (with C. Alfes-Neumann and M. Schwagenscheidt), Math. Ann. 391 (2025), 791–817. pdf.
• Deformations of Theta Integrals and A Conjecture of Gross-Zagier (with Y. Li and T. Yang), Forum of Mathematics, Sigma 13 (2025), e54. pdf.
• Arithmetic volumes of unitary Shimura varieties (with B. Howard), Memoirs of the AMS, to appear. pdf (PDF file) (opens in new tab).
• Special cycles on toroidal compactifications of orthogonal Shimura varieties (with S. Zemel), Math. Ann. 384 (2022), pages 1-63. pdf (PDF file) (opens in new tab).
• CM values of higher automorphic Green functions for orthogonal groups (with S. Ehlen and T. Yang), Invent. Math. 225 (2021), 693-785. pdf (PDF file) (opens in new tab).
• Theta lifts for Lorentzian lattices and coefficients of mock theta functions (with M. Schwagenscheidt), Mathematische Zeitschrift 297 (2021), 1633-1657. pdf (PDF file) (opens in new tab).
• A converse theorem for Borcherds products on X_0(N) (with M. Schwagenscheidt), Nagoya Mathematical Journal 240 (2020), 237-256. pdf (PDF file) (opens in new tab).
• Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series (with T. Yang), Journal of the European Mathematical Society (JEMS) 23 (2021), 1613–1674. pdf (PDF file) (opens in new tab).
• Modularity of generating series of winding numbers (with J. Funke, O. Imamoglu, Yingkun Li), Research in the Mathematical Sciences 5:23 (2018). pdf (PDF file) (opens in new tab).
• Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications (with B. Howard, S. Kudla, M. Rapoprt, and T. Yang), Astérisque 421 (2020), 127-186. pdf (PDF file) (opens in new tab).
• Cones of Heegner divisors (with M. Möller), Journal of Algebraic Geometry 28 (2019), 497-517. pdf (PDF file) (opens in new tab).
• Modularity of generating series of divisors on unitary Shimura varieties (with B. Howard, S. Kudla, M. Rapoport, and T. Yang), Astérisque 421 (2020), 7-125. pdf (PDF file) (opens in new tab).
• Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products (with M. Schwagenscheidt), Journal of Algebra 478 (2017), 38-57. pdf (PDF file) (opens in new tab).
• Borcherds products with prescribed divisor, Bull. London Math. Soc. 49 (2017), 979-987. pdf (PDF file) (opens in new tab).
• Degenerate Whittaker functions for Sp_n(R) (with J. Funke and S. Kudla), Int. Math. Res. Not. IMRN (2018), no. 1, 1–56. pdf (PDF file) (opens in new tab).
• Heegner divisors in generalized Jacobians and traces of singular moduli (with Y. Li), Algebra and Number Theory 10 (2016), 1277-1300. pdf (PDF file) (opens in new tab).
• Kudla's modularity conjecture and formal Fourier-Jacobi series (with M. Raum), Forum of Math. Pi, vol. 3 (2015), 30 pp. pdf, correction: pdf.
• Lattices with many Borcherds products (with S. Ehlen and E. Freitag), Mathematics of Computation, vol. 85, no. 300 (2016), 1953-1981. pdf (PDF file) (opens in new tab).
• Vector valued formal Fourier-Jacobi series, Proc. Amer. Math. Soc. 143 (2015), 505-512. pdf (PDF file) (opens in new tab).
• Heights of Kudla-Rapoport divisors and derivatives of L-functions (with B. Howard and T. Yang), Invent. Math. 201 (2015), 1-95. pdf (PDF file) (opens in new tab).
• Class polynomials for nonholomorphic modular functions (with K. Ono and A. Sutherland), Journal of Number Theory 161 (2016), 204-229. pdf (PDF file) (opens in new tab).
• On the converse theorem for Borcherds products, Journal of Algebra 397 (2014), 315-342. pdf (PDF file) (opens in new tab).
• Regularized theta liftings and periods of modular functions (with J. Funke and O. Imamoglu), J. Reine Angew. Math. 703 (2015), 43-93. pdf (PDF file) (opens in new tab).
• Harmonic Maass forms and periods, Math. Ann. 357 (2013), 1363-1387. pdf (PDF file) (opens in new tab).
• Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms (with K. Ono), Advances in Mathematics 246 (2013), 198-219. pdf (PDF file) (opens in new tab).
• Computation of harmonic weak Maass forms (with F. Strömberg), Experimental Mathematics 21:2 (2012), 117-131. pdf (PDF file) (opens in new tab).
• Special values of Green functions at big CM points (with S. Kudla and T. Yang), Int. Math. Res. Not. 2012:9 (2012), 1917-1967. pdf (PDF file) (opens in new tab).
• CM values of automorphic Green functions on orthogonal groups over totally real fields (with T. Yang). In: Arithmetic Geometry and Automorphic Forms, Eds.: J. Cogdell et. al., Higher Education Press and International Press (2011), 1-54. pdf (PDF file) (opens in new tab).
• Regularized theta lifts for orthogonal groups over totally real fields, J. Reine Angew. Math. 672 (2012), 177-222. pdf (PDF file) (opens in new tab).
• Identities and congruences for Ramanujan's omega(q) (with K. Ono), Ramanujan J. 23 (2010), 151-157. pdf (PDF file) (opens in new tab).
• Faltings heights of CM cycles and derivatives of L-functions (with T. Yang), Invent. Math. 177 (2009), 631-681. pdf (PDF file) (opens in new tab).
• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues (with K. Ono and R. Rhoades), Math. Ann. 342 (2008), 673-693. pdf (PDF file) (opens in new tab), correction: pdf (PDF file) (opens in new tab).
• Heegner divisors, L-functions and harmonic weak Maass forms (with K. Ono), Annals of Math. 172 (2010), 2135-2181. pdf (PDF file) (opens in new tab).
• Sign changes of coefficients of half integral weight modular forms (with W. Kohnen). In: Modular forms on Schiermonnikoog, Eds.: B. Edixhoven, G. van der Geer and B. Moonen, Cambridge University Press (2008), 57-66. pdf (PDF file) (opens in new tab).
• The Weil representation and Hecke operators for vector valued modular forms (with O. Stein), Mathematische Zeitschrift 264 (2010), 249-270. pdf (PDF file) (opens in new tab).
• On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift (with J. Funke). In: Moonshine -- the first quarter century and beyond, Eds.: J. Lepowski, J. McKay, M. Tuite, Cambridge University Press (2010), 12-39. pdf (PDF file) (opens in new tab).
• Twisted Borcherds products on Hilbert modular surfaces and their CM values (with T. Yang), Amer. J. Math. 129 (2007), 807-841. pdf (PDF file) (opens in new tab).
• Hilbert class polynomials and traces of singular moduli (with P. Jenkins and K. Ono), Math. Ann. 334 (2006), 373-393. pdf (PDF file) (opens in new tab).
• Traces of CM-values of modular functions (with Jens Funke), J. Reine Angew. Math. 594 (2006), 1-33. pdf (PDF file) (opens in new tab).
• CM values of Hilbert modular functions (with T. Yang), Invent. Math. 163 (2006), 229-288. pdf (PDF file) (opens in new tab).
• Borcherds products and arithmetic intersection theory on Hilbert modular surfaces (with J. Burgos Gil and U. Kühn), Duke Math. Journal 139 (2007), 1-88. pdf (PDF file) (opens in new tab).
• On Two Geometric Theta Lifts (with J. Funke), Duke Math. Journal 125 (2004), 45-90. pdf (PDF file) (opens in new tab).
• Two applications of the curve lemma for orthogonal groups, Math. Nachr. 274-275 (2004), 19-31. pdf (PDF file) (opens in new tab).
• Integrals of automorphic Green's functions associated to Heegner divisors (with U. Kühn), Int. Math. Res. Not. 2003:31 (2003), 1687-1729. pdf (PDF file) (opens in new tab).
• Coefficients of half-integral weight modular forms (with K. Ono), J. Number Theory 99 (2003), 164-179. pdf (PDF file) (opens in new tab).
• The arithmetic of the values of modular functions and the divisors of modular forms (with W. Kohnen and K. Ono), Compos. Math. 140 (2004), 552-566. pdf (PDF file) (opens in new tab).
• On Borcherds products associated with lattices of prime discriminant (with M. Bundschuh), Ramanujan J. 7 (2003), 49-61. pdf (PDF file) (opens in new tab).
• The arithmetic of Borcherds' exponents (with K. Ono), Math. Ann. 327 (2003), 293-303. pdf (PDF file) (opens in new tab).
• On the rank of Picard groups of modular varieties attached to orthogonal groups, Compos. Math. 133 (2002), 49-63. pdf (PDF file) (opens in new tab).
• Local Borcherds products (with E. Freitag), Ann. Inst. Fourier 51 (2001), 1-27. pdf (PDF file) (opens in new tab).
• Eisenstein series attached to lattices and modular forms on orthogonal groups (with M. Kuss), Manuscr. Math. 106 (2001), 443-459. pdf (PDF file) (opens in new tab).
• Borcherds products and Chern classes of Hirzebruch-Zagier divisors, Invent. Math. 138 (1999), 51-83. pdf (PDF file) (opens in new tab).
• Non-vanishing modulo l of Fourier coefficients of half-integral weight modular forms, Duke Math. Journal 98 (1999), 595-611. pdf (PDF file) (opens in new tab).
• Non-vanishing of scalar products of Fourier-Jacobi coefficients of Siegel cusp forms (with S. Böcherer and W. Kohnen), Math. Ann. 313 (1999), 1-13. pdf (PDF file) (opens in new tab).
• On a theorem of Vigneras, Abh. Math. Sem. Univ. Hamburg 68 (1998), 163-168. pdf (PDF file) (opens in new tab).

Some expository papers

• Recent work on the partition function (with A. Folsom, Z. Kent, and K. Ono), The Legacy of Srinivasa Ramanujan, RMS-Lecture Notes Series No. 20 (2013), pp. 139–151. pdf (PDF file) (opens in new tab).
• The Gross-Zagier formula and the Borcherds lift, Proceedings of the National Institute of Mathematical Sciences 3, No. 10 (2008), 1-8. pdf (PDF file) (opens in new tab).
• Traces of CM-values of modular functions and related topics.
  In: Proceedings of the Conference on “Automorphic Forms and Automorphic L-Functions”, RIMS Kokyuroku 1468, Kyoto (2006). pdf (PDF file) (opens in new tab).
• Infinite products in number theory and geometry, Jahresber. Dtsch. Math. Ver. 106 (2004), Heft 4, 151-184. pdf (PDF file) (opens in new tab).
• Arithmetic Hirzebruch-Zagier divisors and modular forms.
  In: Mathematisches Institut, Seminars, Ed.: Y. Tschinkel, Universität Göttingen (2004), 201-209. pdf (PDF file) (opens in new tab).
• Local Picard groups and theta series.
  In: Proceedings of the Japanese-German Seminar “Explicit Structures of Modular Forms and Zeta Functions”, Eds.: T. Ibukiyama and W. Kohnen, Ryushi-do (2002), 69-73. pdf (PDF file) (opens in new tab).
• Primzahlen, Teilersummen und die Riemannsche Vermutung, Math. Semesterber. 48 (2001), 79-92. pdf (PDF file) (opens in new tab).
• Congruence properties of values of L-functions and applications (with K. James, W. Kohnen, K. Ono, C. Skinner, and V. Vatsal).
  In: Topics in Number Theory (Eds.: S. D. Ahlgren et al.), Kluwer Academic Publishers (1999), 115-125.

Books

• L-Functions and Automorphic Forms. Proceedings of the conference LAF, Heidelberg, February 22-26, 2016 (jointly edited with W. Kohnen). Contributions in Mathematical and Computational Sciences, vol. 10, Springer-Verlag (2017).
• Hilbert modular forms and their applications. Notes of the lectures at the summer school on “Modular Forms and their Applications” at the Sophus Lie Conference Center, Nordfjordeid, Norway. Appeared in: The 1-2-3 of Modular Forms.
• Borcherds products on O(2,l) and Chern classes of Heegner divisors, Springer Lecture Notes in Mathematics 1780, Springer-Verlag (2002), 152 pages. This is a revised version of my Habilitationsschrift (Universität Heidelberg, May 2000). pdf (PDF file) (opens in new tab).

Thesis

• Borcherdsprodukte und Chernsche Klassen von Hirzebruch-Zagier-Zykeln, Dissertation, Universität Heidelberg (1998). pdf (PDF file) (opens in new tab).
• Modulformen halbganzen Gewichtes und Beziehungen zu Dirichletreihen, Diploma thesis, Universität Heidelberg (1997).