26 citations · 113 across the 27 of their papers we have counts for
32 papers
Twisted traces of modular functions on hyperbolic -space
Sebastián Herrero, Özlem Imamoglu, Anna-Maria von Pippich +1
We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic -space and show that they are essentially given by Fourier coefficients of the $j…
Cycle integrals of meromorphic Hilbert modular forms
Claudia Alfes, Baptiste Depouilly, Paul Kiefer +1
We establish a rationality result for linear combinations of traces of cycle integrals of certain meromorphic Hilbert modular forms. These are meromorphic counterparts to the Hilbe…
Special values of Green's functions on hyperbolic -space
Sebastián Herrero, Özlem Imamoglu, Anna-Maria von Pippich +1
Gross, Kohnen and Zagier proved an averaged version of the algebraicity conjecture for special values of higher Green's functions on modular curves. In this work, we study an analo…
Cycle integrals of meromorphic modular forms and Siegel theta functions
Markus Schwagenscheidt
We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the modular curve. We show that suit…
Laurent expansions of meromorphic modular forms
Gabriele Bogo, Yingkun Li, Markus Schwagenscheidt
In this paper, we study the Laurent coefficients of meromorphic modular forms at CM points by giving two approaches of computing them. The first is a generalization of the method o…
Binary theta functions and Borcherds products
Markus Schwagenscheidt, Brandon Williams
We obtain infinite product expansions in the sense of Borcherds for theta functions associated with certain positive-definite binary quadratic and binary hermitian forms. Among oth…
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,…
Harmonic weak Maass forms and periods II
Claudia Alfes-Neumann, Jan Hendrik Bruinier, Markus Schwagenscheidt
In this paper we investigate the Fourier coefficients of harmonic Maass forms of negative half-integral weight. We relate the algebraicity of these coefficients to the algebraicity…
Cycle Integrals of the Parson Poincaré Series and Intersection Angles of Geodesics on Modular Curves
Alessandro Lägeler, Markus Schwagenscheidt
We prove a geometric formula for the cycle integrals of Parson's weight 2k modular integrals in terms of the intersection angles of geodesics on modular curves. Our result is an an…
Mock Modular Forms with Integral Fourier Coefficients
Yingkun Li, Markus Schwagenscheidt
In this note, we explicitly construct mock modular forms with integral Fourier coefficients by evaluating regularized Petersson inner products involving their shadows, which are un…
Arithmetic properties of Fourier coefficients of meromorphic modular forms
Steffen Löbrich, Markus Schwagenscheidt
We investigate integrality and divisibility properties of Fourier coefficients of meromorphic modular forms of weight associated to positive definite integral binary quadratic…
Locally harmonic Maass forms and periods of meromorphic modular forms
Steffen Löbrich, Markus Schwagenscheidt
We investigate a new family of locally harmonic Maass forms which correspond to periods of modular forms. They transform like negative weight modular forms and are harmonic apart f…
Cycle integrals of meromorphic modular forms and coefficients of harmonic Maass forms
Claudia Alfes-Neumann, Kathrin Bringmann, Joshua Males +1
In this paper, we investigate traces of cycle integrals of certain meromorphic modular forms. By relating them to regularised theta lifts we provide explicit formulae for them in t…
Rigidity of elliptic genera: from number theory to geometry and back
Kathrin Bringmann, Alexander Caviedes Castro, Silvia Sabatini +1
In this paper we derive topological and number theoretical consequences of the rigidity of elliptic genera, which are special modular forms associated to each compact almost comple…
Theta lifts for Lorentzian lattices and coefficients of mock theta functions
Jan Hendrik Bruinier, Markus Schwagenscheidt
We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of…
Meromorphic modular forms with rational cycle integrals
Steffen Löbrich, Markus Schwagenscheidt
We study rationality properties of geodesic cycle integrals of meromorphic modular forms associated to positive definite binary quadratic forms. In particular, we obtain finite rat…
Traces of reciprocal singular moduli
Claudia Alfes-Neumann, Markus Schwagenscheidt
We show that the generating series of traces of reciprocal singular moduli is a mixed mock modular form of weight whose shadow is given by a linear combination of products of…
Twisted component sums of vector-valued modular forms
Markus Schwagenscheidt, Brandon Williams
We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the unde…
Identities of Cycle Integrals of Weak Maass Forms
Claudia Alfes-Neumann, Markus Schwagenscheidt
We prove identities between cycle integrals of non-holomorphic modular forms arising from applications of various differential operators to weak Maass forms.
Holomorphic Borcherds products of singular weight for simple lattices of arbitrary level
Sebastian Opitz, Markus Schwagenscheidt
We classify the holomorphic Borcherds products of singular weight for all simple lattices of signature with . In addition to the automorphic products of singular…
On the rationality of cycle integrals of meromorphic modular forms
Claudia Alfes-Neumann, Kathrin Bringmann, Markus Schwagenscheidt
We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating funct…
Nonvanishing modulo of Fourier coefficients of Jacobi forms
Markus Schwagenscheidt
Let be a Jacobi form of weight (with if is not a cusp form) and index with integral algebraic coefficients which is a…
Borcherds lifts of harmonic Maass forms and modular integrals
Markus Schwagenscheidt
We extend Borcherds' singular theta lift in signature to harmonic Maass forms of weight whose non-holomorphic part is allowed to be of exponential growth at …
A converse theorem for Borcherds products on
Jan Hendrik Bruinier, Markus Schwagenscheidt
We show that every Fricke invariant meromorphic modular form for whose divisor on is defined over and supported on Heegner divisors and the cusps is…