Publications - Jan H. Bruinier

Research papers and preprints

Vector valued formal Fourier-Jacobi series, preprint (2013).
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Heights of Kudla-Rapoport divisors and derivatives of L-functions (with B. Howard and T. Yang), preprint (2013).
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Class polynomials for nonholomorphic modular functions (with K. Ono and A. Sutherland), preprint (2013).
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On the converse theorem for Borcherds products, preprint (2012).
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Regularized theta liftings and periods of modular functions (with J. Funke and O. Imamoglu), preprint (2012).
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Harmonic Maass forms and periods, Math. Ann., accepted for publication.
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Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms (with K. Ono), preprint (2011).
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Computation of harmonic weak Maass forms (with F. Strömberg), Experimental Mathematics 21:2 (2012), 117-131.
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Special values of Green functions at big CM points (with S. Kudla and T. Yang), Int. Math. Res. Not. 2012:9 (2012), 1917-1967.
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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.
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Regularized theta lifts for orthogonal groups over totally real fields, J. Reine Angew. Math. 672 (2012), 177-222.
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Identities and congruences for Ramanujan's omega(q) (with K. Ono), Ramanujan J. 23 (2010), 151-157.
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Faltings heights of CM cycles and derivatives of L-functions (with T. Yang), Invent. Math. 177 (2009), 631-681.
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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.
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Heegner divisors, L-functions and harmonic weak Maass forms (with K. Ono), Annals of Math. 172 (2010), 2135-2181.
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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.
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The Weil representation and Hecke operators for vector valued modular forms (with O. Stein), Mathematische Zeitschrift 264 (2010), 249-270.
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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.
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Twisted Borcherds products on Hilbert modular surfaces and their CM values (with T. Yang), Amer. J. Math. 129 (2007), 807-841.
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Hilbert class polynomials and traces of singular moduli (with P. Jenkins and K. Ono), Math. Ann. 334 (2006), 373-393.
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Traces of CM-values of modular functions (with Jens Funke), J. Reine Angew. Math. 594 (2006), 1-33.
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CM values of Hilbert modular functions (with T. Yang), Invent. Math. 163 (2006), 229-288.
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Borcherds products and arithmetic intersection theory on Hilbert modular surfaces (with J. Burgos Gil and U. Kühn), Duke Math. Journal 139 (2007), 1-88.
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On Two Geometric Theta Lifts (with J. Funke), Duke Math. Journal 125 (2004), 45-90.
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Two applications of the curve lemma for orthogonal groups, Math. Nachr. 274-275 (2004), 19-31.
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Integrals of automorphic Green's functions associated to Heegner divisors (with U. Kühn), Int. Math. Res. Not. 2003:31 (2003), 1687-1729.
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Coefficients of half-integral weight modular forms (with K. Ono), J. Number Theory 99 (2003), 164-179.
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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.
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On Borcherds products associated with lattices of prime discriminant (with M. Bundschuh), Ramanujan J. 7 (2003), 49-61.
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The arithmetic of Borcherds' exponents (with K. Ono), Math. Ann. 327 (2003), 293-303.
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On the rank of Picard groups of modular varieties attached to orthogonal groups, Compos. Math. 133 (2002), 49-63.
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Local Borcherds products (with E. Freitag), Ann. Inst. Fourier 51 (2001), 1-27.
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Eisenstein series attached to lattices and modular forms on orthogonal groups (with M. Kuss), Manuscr. Math. 106 (2001), 443-459.
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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).
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Borcherds products and Chern classes of Hirzebruch-Zagier divisors, Invent. Math. 138 (1999), 51-83.
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Non-vanishing modulo l of Fourier coefficients of half-integral weight modular forms, Duke Math. Journal 98 (1999), 595-611.
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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.
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On a theorem of Vigneras, Abh. Math. Sem. Univ. Hamburg 68 (1998), 163-168.
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Some expository papers

Recent work on the partition function (with A. Folsom, Z. Kent, and K. Ono), preprint (2012).
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The Gross-Zagier formula and the Borcherds lift, Proceedings of the National Institute of Mathematical Sciences 3, No. 10 (2008), 1-8.
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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).
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Infinite products in number theory and geometry, Jahresber. Dtsch. Math. Ver. 106 (2004), Heft 4, 151-184.
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Arithmetic Hirzebruch-Zagier divisors and modular forms.
In: Mathematisches Institut, Seminars, Ed.: Y. Tschinkel, Universität Göttingen (2004), 201-209.
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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.
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Primzahlen, Teilersummen und die Riemannsche Vermutung, Math. Semesterber. 48 (2001), 79-92.
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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.

Lecture notes

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.

Thesis

Borcherdsprodukte und Chernsche Klassen von Hirzebruch-Zagier-Zykeln, Dissertation, Universität Heidelberg (1998).
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Modulformen halbganzen Gewichtes und Beziehungen zu Dirichletreihen, Diploma thesis, Universität Heidelberg (1997).
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