Publications (13)
On the modular completion of certain generating functions
Kathrin Bringmann, Stephan Ehlen, Markus Schwagenscheidt
We complete several generating functions to non-holomorphic modular forms in two variables. For instance, we consider the generating function of a natural family of meromorphic mod…
CM values of higher automorphic Green functions for orthogonal groups
Jan Hendrik Bruinier, Stephan Ehlen, Tonghai Yang
Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function for the elliptic modular group at positive integral s…
Central -values of elliptic curves and local polynomials
Stephan Ehlen, Pavel Guerzhoy, Ben Kane +1
Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of -functions. In particular, we find finite formulas for certai…
Twisted Traces of CM values of Harmonic Weak Maass Forms
Claudia Alfes, Stephan Ehlen
We show that the twisted traces of CM values of weak Maass forms of weight 0 are Fourier coefficients of vector valued weak Maass forms of weight 3/2. These results generalize work…
On two arithmetic theta lifts
Stephan Ehlen, Siddarth Sankaran
Our aim is to clarify the relationship between Kudla's and Bruinier's Green functions attached to special cycles on Shimura varieties of orthogonal and unitary type. These function…
CM values of regularized theta lifts and harmonic weak Maaà forms of weight one
Stephan Ehlen
We study special values of regularized theta lifts at complex multiplication (CM) points. In particular, we show that CM values of Borcherds products can be expressed in terms of f…
Computing Invariants of the Weil representation
Stephan Ehlen, Nils-Peter Skoruppa
We propose an algorithm for computing bases and dimensions of spaces of invariants of Weil representations of associated to finite quadratic modules. We…
Regularized inner products and errors of modularity
Kathrin Bringmann, Nikolaos Diamantis, Stephan Ehlen
We develop a regularization for Petersson inner products of arbitrary weakly holomorphic modular forms, generalizing several known regularizations. As one application, we extend wo…
On CM values of Borcherds products and harmonic weak Maass forms of weight one
Stephan Ehlen
We show that the values of Borcherds products on Shimura varieties of orthogonal type at certain CM points are given in terms of coefficients of the holomorphic part of weight one…
Lattices with many Borcherds products
Jan Hendrik Bruinier, Stephan Ehlen, Eberhard Freitag
We prove that there are only finitely many isometry classes of even lattices of signature for which the space of cusp forms of weight for the Weil representatio…
Harmonic Maass forms associated with CM newforms
Stephan Ehlen, Yingkun Li, Markus Schwagenscheidt
In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight under the -operator. As a result…
Vector valued theta functions associated with binary quadratic forms
Stephan Ehlen
We study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relat…
Singular moduli of higher level and special cycles
Stephan Ehlen
We describe the complex multiplication (CM) values of modular functions for whose divisor is given by a linear combination of Heegner divisors in terms of special cycles…