8 citations · 18 across the 7 of their papers we have counts for
7 papers · 1 filter
Twisted Borcherds products on Hilbert modular surfaces and their CM values
Jan Hendrik Bruinier, Tonghai Yang
We construct a natural family of rational functions on a Hilbert modular surface from the classical -invariant and its Hecke translates. These functions are obtained…
Traces of CM values of modular functions
Jan Hendrik Bruinier, Jens Funke
Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modula…
Infinite products in number theory and geometry
Jan Hendrik Bruinier
We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study t…
Borcherds products and arithmetic intersection theory on Hilbert modular surfaces
Jan H. Bruinier, Jose I. Burgos Gil, Ulf Kuehn
We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular…
On Borcherds products associated with lattices of prime discriminant
Jan H. Bruinier, M. Bundschuh
We show that certain spaces of vector valued modular forms are isomorphic to spaces of scalar valued modular forms whose Fourier coefficients are supported on suitable progressions…
Two applications of the curve lemma for orthogonal groups
Jan H. Bruinier
We show (under some hypothesis in small dimensions) that the analytic degree of the divisor of a modular form on the orthogonal group O(2,p) is determined by its weight. Moreover,…