Dr. Andreas Mono

1. A modular framework for generalized Hurwitz class numbers II (with Olivia Beckwith)

preprint (2024), submitted for publication

arXiv.org:2411.07962

2. A modular framework for generalized Hurwitz class numbers I (with Olivia Beckwith)

preprint (2024), submitted for publication

arxiv.org:2403.17829

3. Central L-values of newforms and local polynomials (with Joshua Males, Larry Rolen, and Ian Wagner)

preprint (2023), submitted for publication

arxiv.org:2306.15519

4. Linear congruence relations for exponents of Borcherds products (with Badri Vishal Pandey)

preprint (2023), submitted for publication

arxiv.org:2301.11184

5. A modular framework of functions of Knopp and indefinite binary quadratic forms (with Kathrin Bringmann)

preprint (2022), submitted for publication

arxiv.org:2208.01451

6. Locally harmonic Maaß forms of positive even weight

Israel Journal of Mathematics 261 (2024), no. 2, 671–-694

https://doi.org/10.1007/s11856-023-2592-7

7. Correction to the article Local Maaß forms and Eichler-Selberg type relations for negative weight vector-valued mock modular forms (with Joshua Males)

Pacific Journal of Mathematics 332 (2024), no. 2, 395--396

https://doi.org/10.2140/pjm.2024.332.395

8. Local Maaß forms and Eichler-Selberg type relations for negative weight vector-valued mock modular forms (with Joshua Males)

Pacific Journal of Mathematics 322 (2023), no. 2, 381--406

https://doi.org/10.2140/pjm.2023.322.381

9. Eisenstein series of even weight k>=2 and integral binary quadratic forms

Proceedings of the American Mathematical Society 150 (2022), 1889--1902

https://doi.org/10.1090/proc/15617

10. Higher depth mock theta functions and q-hypergeometric series (with Joshua Males and Larry Rolen)

Forum Mathematicum 33 (2021), no. 4, 857--866

https://doi.org/10.1515/forum-2021-0013

11.  Multidimensional small divisor functions

Integers 21 (2021), Paper No. A104

https://doi.org/10.5281/zenodo.10839396

12. Polar harmonic Maaß forms and holomorphic projection (with Joshua Males and Larry Rolen)

International Journal of Number Theory 18 (2022), no. 9, 1975--2004

https://doi.org/10.1142/S1793042122501019

13.  On a conjecture of Kaneko and Koike

preprint (2020)

arxiv.org:2005.06882

• My PhD thesis

• My Master thesis 

• Co-organizer of the "International conference on L-functions and automorphic forms" joint with  Larry Rolen and Jesse Thorner as part of Vanderbilt's Shanks conference series,  May 13th to May 16th 2024.

• Mentor in the Directed Reading Program at Vanderbilt University since the Spring semester 2024.

• Co-organizer of the Early Number Theory Researchers (ENTR) Workshop joint with Giulia Cesana, Ingmar Metzler, Riccardo Zuffetti and Lars Kleinemeier, October 2022.

• Co-organizer of the Early Number Theory Researchers (ENTR) Seminar joint with Giulia Cesana and Ingmar Metzler, Spring semester 2022.

• Mentor of a very talented teenager in Analysis I, II and III, Fall semester 2021, Spring Semester 2022, Fall Semester 2022.

• Referee:

1. Archiv der Mathematik (two times)

2. International Journal of Number Theory (two times)

3. Proceedings of the American Mathematical Society

4. Research in the Mathematical Sciences

5. Research in Number Theory (three times) 

6. The Ramanujan Journal (three times)

• Course instructor (with Joshua Males), Junior Uni Cologne, awarded a small outreach grant, March and April 2021.

• Algebra, Geometry, and Number Theory Seminar, University of South Carolina, September 27 2024. 

• International Conference on Modular Forms and q-Series , University of Cologne, Speedtalk, March 12 2024.

• The web of modularity, Clifford lectures, Tulane University, February 24 2024.

• Vanderbilt Undergraduate Seminar in Mathematics,  Vanderbilt University, October 24, 2023.

• Palmetto Number Theory Series XXXVI, in memoriam of Kevin James, Clemson University, October 21, 2023.

• Vanderbilt Number Theory Seminar, Vanderbilt University, October 3, 2023.

• 35th Automorphic Forms Workshop, Louisiana State University, May 24, 2023.

• Ramanujan-Serre Seminar, University of Virginia, September 16, 2022.

• Ramanujan and Euler: Partitions, mock theta functions, and q-series, July 22, 2022.

• 100 Years of Mock Theta Functions, Vanderbilt University, Speedtalk, May 23, 2022.

• Young Scholars in the Analytic Theory of Numbers and Automorphic Forms (Fantasy), University of Bonn, March 28, 2022.

• 34th Automorphic Forms Workshop, awarded a small amount of prize money, March 18, 2022.

• JENTE seminar, November 09, 2021.

• CDE Seminar,  June 14, 2021.

• International Seminar on Automorphic Forms, April 20, 2021.

• Number Theory Lunch Seminar, Max Planck Institute Bonn, February 10, 2021.

• Oberseminar Geometrische Analysis und Zahlentheorie, Paderborn, February 02, 2021.

• PhD Seminar Geometrische Analysis und Zahlentheorie, Paderborn, January 28, 2021.

• International Conference on Modular Forms and q-Series , University of Cologne, March 2024.

• The web of modularity, Clifford lectures, Tulane University, February 2024.

• Palmetto Number Theory Series XXXVI, in memoriam of Kevin James, Clemson University, October 2023.

• 35th Automorphic Forms Workshop, May 2023.

• Research visit to University of Virginia, Charlottesville, USA, during September 2022.

• Research visit to Vanderbilt University, Nashville, USA, during August 2022.

• 100 Years of Mock Theta Functions, May 2022.

• Young Scholars in the Analytic Theory of Numbers and Automorphic Forms (Fantasy), March 2022.

• 34th Automorphic Forms Workshop, March 2022.

• 5th Number Theory Meeting, October 2021.

• New connections in number theory and physics, May 2021.

Lecturer / Instructor:

• "Number Theory", Vanderbilt University, Spring semester 2025

• "Number Theory", Vanderbilt University, Fall semester 2024

• "Accelerated Calculus II", Vanderbilt University, Spring semester 2024

• ''Linear Algebra II'', University of Cologne, Spring Semester 2021.

• ''Analysis I + II'', ETH Zurich, exam preparation course, June 2016. 

Coordinator:

• ''Elementary Number Theory'', University of Cologne, Spring Semester 2022.

• ''Algebra'', University of Cologne, Fall Semester 2021.

• ''Linear Algebra II'', University of Cologne, Spring Semester 2021.

• ''Linear Algebra I'', University of Cologne, Fall Semester 2020.

 Co-supervised student theses:

• "Elliptic curves and the elliptic curve group", Ethan Sherman, Vanderbilt University, 2024

• ''The generating function of Hurwitz class numbers and its connection to mock modular forms'', Jakob Sauer, Bachelor thesis, University of Cologne, 2022--2024.

• ''Supercongruences'', Hei Loi Lin, Bachelor thesis, University of Cologne, 2021.

• ''Nonholomorphic Eisenstein series'', Lukas Gebert, Master thesis, University of Cologne, 2020.

Co-supervised student seminars:

•  ''Theta functions'', University of Cologne, Fall semester 2022. 

•  ''Modular forms'', University of Cologne, Spring semster 2020.

Teaching assistant:

• "Accelerated Calculus II", Vanderbilt University, Fall semester 2023

• ''Algebra'', University of Cologne, Fall semester 2022. 

• ''Algebra'', University of Cologne, Fall semester 2021. 

• ''Linear Algebra II'', University of Cologne, Spring Semester 2021.

• ''Linear Algebra I'', University of Cologne, Fall Semester 2020.

• ''Complex Analysis'', University of Cologne, Spring Semester 2020.

• ''Complex Analysis'', ETH Zurich, Fall Semester 2018.

• ''Measure and Integration'', ETH Zurich, Spring Semester 2018.

• ''Complex Analysis'', awarded by the Mathematicians and Physicists Association at ETH Zurich, ETH Zurich, Fall Semester 2017.

• ''Analysis II'', ETH Zurich, Spring Semester 2017.

• ''Analysis I'', ETH Zurich, Fall Semester 2016.