Publications

Published papers

Most of the linked pdf-files here are preprints and may differ from the published version of the paper.
  1. (with Markus Kirschmer) "On an Analogue to the Lucas-Lehmer-Riesel Test using Elliptic Curves", pdf, Integers (2013), 13 A15.
  2. "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.
  3. "Mock Modular Forms and Class Number Relations", pdf, Research in the Mathematical Sciences.2014, 1:6
  4. "Eichler-Selberg Type Identities for Mixed Mock Modular Forms", pdf, Advances in Mathematics 301 (2016), pp. 359-382.
  5. (with Jehanne Dousse) "Asymptotic Formulas for Partition Ranks", pdf, Acta Arithmetica 168 (2015), pp. 83-100.
  6. (with Ken Ono) "Special values for shifted convolution Dirichlet series", pdf, Mathematika 62 (2016), pp. 47-66.
  7. (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.
  8. (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).
  9. (with Larry Rolen) "Lacunary recurrences for Eisenstein series", pdf, Research in Number Theory 1:9 (2015).
  10. (with Olivia Beckwith) "The number of parts in certain residue classes of integer partitions",pdf, Research in Number Theory 1:11 (2015).
  11. (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.
  12. (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.
  13. (with John F. R. Duncan and K. Ono) "O'Nan moonshine and arithmetic", American Journal of Mathematics 143 (2021), No. 4, 1115-1159.
  14. (with John F. R. Duncan and Ken Ono) "Pariah moonshine", pdf, Nature Communications 8, Article number 670 (2017).
  15. (with Pavel Guerzhoy and Larry Rolen) "Periodicity of Taylor coefficients of half-integer weight modular forms", Pacific Journal of Mathematics 307 (2020), 137-157.
  16. (with Lea Beneish) "On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras", Mathematische Zeitschrift 297 (2021), 59-80.
  17. (with Martin Raum) "Modular forms of virtually arithmetic types I", Mathematical Research Letters 28 (2021), 511-561.
  18. (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.
  19. (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.
  20. (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.
  21. (with Geoffrey Mason) "1-point functions for symmetrized Heisenberg and lattice VOAs", Transactions of the AMS 276 (2023), 3663-3693.

Preprints

  1. (with Claudia Alfes-Neumann, Jens Funke, and Eugenia Rosu) "On Jacobi-Weierstrass mock modular forms", submitted for publication.
  2. (with Mark A. Norfleet) "Weight 1/2 multiplier systems for the group Γ0+(p) and a geometric interpretation", submitted for publication.
  3. (with Kathrin Bringmann and Ben Kane) "Hecke eigenforms for meromorphic cusp forms", submitted for publication.

Theses

  1. Bachelor Thesis: "Primzahltests mit Elliptischen Kurven", pdf, 2011, supervised by Prof. Dr. Gabriele Nebe, Lehrstuhl D für Mathematik, RWTH Aachen University
  2. Master Thesis: "Duale Kegel und Automorphismengruppen Hyperbolischer Gitter", pdf, 2012, supervised by Prof. Dr. Gabriele Nebe, Lehrstuhl D für Mathematik, RWTH Aachen University
  3. PhD Thesis: "Mock Modular Forms and Class Numbers of Quadratic Forms", 2014, available here, supervised by Prof. Dr. Kathrin Bringmann, Universität zu Köln
  4. 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

  1. Elementare Zahlentheorie (in German), 293 pages, Logos Verlag Berlin, 2019 (ISBN 978-3-8325-4886-5).

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