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Jan Hendrik Bruinier

  1. Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms.

    Пт, 04/08/2011 - 15:01 — SomNambul
    Authors: Jan Hendrik Bruinier, Ken Ono
    Subjects: Number Theory
    Abstract

    We prove that the coefficients of certain weight -1/2 harmonic Maass forms
    are traces of singular moduli for weak Maass forms. To prove this theorem, we
    construct a theta lift from spaces of weight -2 harmonic weak Maass forms to
    spaces of weight -1/2 vector-valued harmonic weak Maass forms on Mp_2(Z), a
    result which is of independent interest. We then prove a general theorem which
    guarantees (with bounded denominator) when such Maass singular moduli are
    algebraic.

  2. Faltings heights of big CM cycles and derivatives of L-functions.

    Ср, 08/11/2010 - 15:01 — SomNambul
    Authors: Jan Hendrik Bruinier, Stephen S. Kudla, Tonghai Yang
    Subjects: Number Theory
    Abstract

    We give a formula for the values of automorphic Green functions on the
    special rational 0-cycles (big CM points) attached to certain maximal tori in
    the Shimura varieties associated to rational quadratic spaces of signature
    (2d,2). Our approach depends on the fact that the Green functions in question
    are constructed as regularized theta lifts of harmonic weak Mass forms, and it
    involves the Siegel-Weil formula and the central derivatives of incoherent
    Eisenstein series for totally real fields.

  3. Regularized theta lifts for orthogonal groups over totally real fields.

    Пнд, 08/24/2009 - 13:10 — SomNambul
    Authors: Jan Hendrik Bruinier
    Subjects: Number Theory
    Abstract

    We define a regularized theta lift for orthogonal groups over totally real
    fields generalizing work of Borcherds. The lift takes harmonic `Whittaker
    forms' to automorphic Green functions and weakly holomorphic Whittaker forms to
    meromorphic modular forms on orthogonal groups with zeros and poles supported
    on special divisors.

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