Publications
Published papers
Most of the linked pdf-files here are preprints and may differ from the published version of the paper.
- (with Markus Kirschmer) "On an Analogue to the Lucas-Lehmer-Riesel Test using Elliptic Curves", pdf, Integers (2013), 13 A15.
- "Automorphism Groups of Hyperbolic Lattices", pdf, Journal of Algebra 408 (2014), pp. 147-165.
The MAGMA-package AutHyp.m
can be downloaded here. Look here for a short description of its main intrinsics.
- "Mock Modular Forms and Class Number Relations", pdf, Research in the Mathematical Sciences.2014, 1:6
- "Eichler-Selberg Type Identities for Mixed Mock Modular Forms", pdf, Advances in Mathematics 301 (2016), pp. 359-382.
- (with Jehanne Dousse) "Asymptotic Formulas for Partition Ranks", pdf, Acta Arithmetica 168 (2015), pp. 83-100.
- (with Ken Ono) "Special values for shifted convolution Dirichlet series", pdf, Mathematika 62 (2016), pp. 47-66.
- (with Kathrin Bringmann and Ken Ono) "p-adic properties of modular shifted convolution L-functions", pdf, Proceedings of the AMS 144 (2016), pp. 1439-1452.
- (with Larry Rolen) "On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono", pdf, Research in Number Theory 1:4 (2015).
- (with Larry Rolen) "Lacunary recurrences for Eisenstein series", pdf, Research in Number Theory 1:9 (2015).
- (with Olivia Beckwith) "The number of parts in certain residue classes of integer partitions",pdf, Research in Number Theory 1:11 (2015).
- (with Olivia Beckwith) "On the number of parts of integer partitions lying in given residue classes", pdf, Annals of Combinatorics 21 (2017), pp. 507-517.
- (with Michael J. Griffin) "A proof of the Thompson Moonshine Conjecture", pdf, Research in the Mathematical Sciences 3:36 (2016).
The relevant MAGMA files can be downloaded as tarballs: Identifyq.tar.gz and Multipliers.tar.gz. Further data and documentation can be found here.
- (with John F. R. Duncan and K. Ono) "O'Nan moonshine and arithmetic", American Journal of Mathematics 143 (2021), No. 4, 1115-1159.
- (with John F. R. Duncan and Ken Ono) "Pariah moonshine", pdf, Nature Communications 8, Article number 670 (2017).
- (with Pavel Guerzhoy and Larry Rolen) "Periodicity of Taylor coefficients of half-integer weight modular forms", Pacific Journal of Mathematics 307 (2020), 137-157.
- (with Lea Beneish) "On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras", Mathematische Zeitschrift 297 (2021), 59-80.
- (with Martin Raum) "Modular forms of virtually arithmetic types I", Mathematical Research Letters 28 (2021), 511-561.
- (with Ken Ono and Larry Rolen) "Mock modular Eisenstein series with Nebentypus", International Journal of Number Theory 17 (2021), Special Issue II: In honor of Bruce Berndt's 80th birthday, 683-697.
- (with Letong Hong, Ken Ono, and Shengtong Zhang) "Proof of the elliptic expansion Moonshine conjecture by Căldăraru, He, and Huang", Proceedings of the AMS 150 (2022), 5047-5056.
- (with Miranda C. N. Cheng and John F. R. Duncan) "Class numbers, Cyclic Simple Groups and Arithmetic", To appear in Journal of the London Mathematical Society.
- (with Geoffrey Mason) "1-point functions for symmetrized Heisenberg and lattice VOAs", Transactions of the AMS 276 (2023), 3663-3693.
Preprints
- (with Claudia Alfes-Neumann, Jens Funke, and Eugenia Rosu) "On Jacobi-Weierstrass mock modular forms", submitted for publication.
- (with Mark A. Norfleet) "Weight 1/2 multiplier systems for the group Γ0+(p) and a geometric interpretation", submitted for publication.
- (with Kathrin Bringmann and Ben Kane) "Hecke eigenforms for meromorphic cusp forms", submitted for publication.
Theses
- Bachelor Thesis: "Primzahltests mit Elliptischen Kurven", pdf, 2011, supervised by Prof. Dr. Gabriele Nebe, Lehrstuhl D für Mathematik, RWTH Aachen University
- Master Thesis: "Duale Kegel und Automorphismengruppen Hyperbolischer Gitter", pdf, 2012, supervised by Prof. Dr. Gabriele Nebe, Lehrstuhl D für Mathematik, RWTH Aachen University
- PhD Thesis: "Mock Modular Forms and Class Numbers of Quadratic Forms", 2014, available here, supervised by Prof. Dr. Kathrin Bringmann, Universität zu Köln
- Habilitation Thesis: "Some applications of singular moduli and complex multliplication", pdf, 2019, Universität zu Köln.
Note: The pdf linked above does not contain copies of the included papers (items 8, 12, and 13 above) making up the main contents of the Habilitation thesis.
Books
- Elementare Zahlentheorie (in German), 293 pages, Logos Verlag Berlin, 2019 (ISBN 978-3-8325-4886-5).