Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors

By Jan H. Bruinier. 2002

440 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/932c3d73ffbc16542efe1ee594cc11b431a8e5b6

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Citations in the corpus

On Borcherds Products Associated with Lattices of Prime Discriminant (2003, methodology): “There the exponents are given by the coefficients of nearly holomorphic Poincar´ e series of weight 2. Using non-holomorphic Poincar´ e series of weight 0 as in [ 3 ], these coefficients could be related to the coefficients of nearly holomorphic modular forms of weight 0. But this requires a conside”
On the converse theorem for Borcherds products (2012, methodology): “ns on the content of this paper. 2. Preliminaries Here we brieﬂy summarize some facts on lattices, discriminant forms, and the Weil representation. For more details we refer to [Bo2], [Sch1], [Sch2], [Br1]. Let (L,Q) be a non-degenerate even lattice of signature (b+,b−). We denote by (·,·) the bilin”
Generalized moonshine, II: Borcherds products (2009, background): “the above formula is zero. Hence, 2jw v+j K(v;F ) = 0, and this is 8ˇ. We can write v = mw0+ nw, so v2 = 2mn = 1, w v += mv, jw v j= m, and jw0 v+ j= n= 1=2m. Then ( mw0+ nw;F K) = 8 p 2ˇn. Following [Bruinier-2002], we dene for each 2K_;n < 0, a distinguished set of points H(;n) = f?jc (n) 6= 0”
Unearthing the visions of a master: harmonic Maass forms and number theory (2008, result): “They also recover some results of Bruinier, Hejhal, and Niebur [62] [117] [160] [161] for harmonic Maass forms of non-positive weight.”
Eisenstein series attached to lattices¶and modular forms on orthogonal groups (2001, methodology): “In this section we briefly recall from [ Br1 ] and [Bo2] some facts about the Weil representation and certain vector valued modular forms.”
Traces of CM values of modular functions (2004, background): “Hence Rk 2Lk 1⁄4 D 0 k, where D 0 k is the weight k Laplacian for t A H as in [4].”
K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space (2004, neutral): “Notice that our HΛ(∞, k) is the half of HΛ(∞, k) in [14].”
Faltings heights of abelian varieties with complex multiplication (2015, methodology): “ealizations (4.1.4) V? ↪ EndC(L)(H?). For x∈ V of positive length, deﬁne a divisor on D by D(x) = {z∈ D ∶ z⊥ x}. FALTINGS HEIGHTS OF ABELIAN VARIETIES 41 As in the work of Borcherds [Bor98], Bruinier [Bru02], and Kudla [Kud04], for every m∈ Q>0 and µ∈ L∨~Lwe deﬁne a complex orbifold Z(m,µ)(C) = +”
Heegner divisors, $L$-functions and harmonic weak Maass forms (2007, methodology): “ined as liftings of weight 1/2 harmonic weak Maass forms f. To deﬁne these liftings, in Section 5 we generalize the regularized theta lift due to Borcherds, Harvey, and Moore (for example, see [Bo1], [Br]). We then employ transcendence results of Waldschmidt and Scholl (see [W], [Sch]), for the peri”
On two geometric theta lifts (2002, methodology): “h,n= {x∈ L+h; q(x) = n} with ﬁnitely many orbits, and we deﬁne the composite cycle Z(h,n) = X x∈Γ\Lh,n Z(x). Occasionally, we will identify Z(h,n) with its preimage in D. Borcherds [Bo2] and Bruinier [Br1] (for O(2,p)) use vectors of negative length to deﬁne special cycles (which are divisors in tha”