papers

Publications (13)

math.NT2018

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…

math.NT2021

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…

math.NT2019

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…

math.NT2013

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…

math.NT2018

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…

math.NT2017

CM values of regularized theta lifts and harmonic weak Maaß 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…

math.NT2017

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…

math.NT2016

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…

math.NT2012

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…

math.NT2015

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…

math.NT2025

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…

math.NT2015

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…

math.NT2015

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…