# Markus Schwagenscheidt

PostDoc in Mathematics

## Publications

Here you can find a list of my research articles.

- Meromorphic modular forms with rational cycle integrals (with Steffen Löbrich),

preprint (2019), arxiv - Traces of reciprocal singular moduli (with Claudia Alfes-Neumann),

preprint (2019), arxiv - Twisted component sums of vector-valued modular forms (with Brandon Williams),

preprint (2019), arxiv - Identities of cycle integrals of weak Maass forms (with Claudia Alfes-Neumann),
*Ramanujan Journal*, accepted for publication (2019), arxiv - On the rationality of cycle integrals of meromorphic modular forms (with Claudia Alfes-Neumann and Kathrin Bringmann),

preprint (2018), arxiv - Holomorphic Borcherds products of singular weight for simple lattices of arbitrary level (with Sebastian Opitz),
*Proceedings of the AMS*, accepted for publication (2019), arxiv - Borcherds lifts of harmonic Maass forms and modular integrals,

preprint (2018), arxiv - A converse theorem for Borcherds products on X_0(N) (with Jan Hendrik Bruinier),
*Nagoya Mathematical Journal*, accepted for publication (2019), arxiv - On the modular completion of certain non-holomorphic generating functions (with Kathrin Bringmann and Stephan Ehlen),

preprint (2018), arxiv - Eisenstein series for the Weil representation,

*Journal of Number Theory*, Vol. 193 (2018), pp 74-90, arxiv - Shintani theta lifts of harmonic Maass forms (with Claudia Alfes-Neumann),

preprint (2018), arxiv - Kronecker limit formulas for parabolic, hyperbolic, and elliptic Eisenstein series via Borcherds products (with Anna-Maria von Pippich and Fabian Völz),

preprint (2017), arxiv - Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products (with Jan Hendrik Bruinier),
*Journal of Algebra*, Vol 478 (2017), pp. 38–57, arxiv - On a theta lift related to the Shintani lift (with Claudia Alfes-Neumann),
*Advances in Mathematics*, Vol. 328 (2018), pp. 858-889, arxiv - Nonvanishing and central critical values of twisted L-functions of cusp forms on average,
*Functiones et Approximatio*, Vol. 55, Issue 1, pp. 45-58 (2016), arxiv - Nonvanishing mod l of Fourier coefficients of Jacobi forms,
*Research in Number Theory*, Vol. 2, Issue 1 (2016), pp. 1-18 (open access) - Lifting newforms to vector valued modular forms for the Weil representation (with Fabian Völz),
*International Journal of Number Theory*, Vol. 11, Issue 7 (2015), pp. 2199-2219 - Automorphic products of singular weight for simple lattices (with Moritz Dittmann and Heike Hagemeier),
*Mathematische Zeitschrift*, Vol. 279, Issue 1 (2015), pp. 585-603, arxiv

### Theses

- Regularized Theta Lifts of Harmonic Maass Forms (supervisor: Jan Hendrik Bruinier), PhD thesis, TU Darmstadt, 2018
- Automorphe Produkte singulären Gewichts zu einfachen Gittern von Primzahlstufe (supervisor: Nils Scheithauer), Master's thesis, TU Darmstadt, 2013