## Dr. Johann FrankeMathematics InstituteUniversity of Cologne Weyertal 86-90 50931 Cologne Germany |
Office: Gyrhofstr. 8b 0.5 Telephone: +49 (0)221 470 1886 Office hours: Nach Vereinbarung E-mail: jfrank12 AT uni-koeln DOT de |

In 2020, I finished my PhD in mathematics under the supervision of Winfried Kohnen at the University of Heidelberg. After a short teaching stint at DHBW Mannheim from April to October 2020, I have been working in Kathrin Bringmann's research group at the University of Cologne since November 2020. My research interests cover analytic and probabilistic number theory and modular forms.

I am one of the organizers of the International conference on modular forms and q-series, that will take place from March 11-15, 2024 at the University of Cologne.

Lebenslauf

L-series of Eisenstein series vanishing at critical values, preprint.

Asymptotics of commuting l-tuples in symmetric groups and log-concavity (with Kathrin Bringmann and Bernhard Heim), preprint.

On the proportion of coprime fractions in number fields (with Walter Bridges and Johann Christian Stumpenhusen), preprint.

On the number of irreducible representations of SU(3) (with Walter Bridges and Kathrin Bringmann), accepted for publication in Acta Arithmetica.

The Approximation of Inverse Functions of Dirichlet Series by Rational Functions, In: N. J. Daras, P. M. Pardalos and M. T. Rassias (eds.), Analysis, Cryptography and Information Science, Series on Computers and Operations Research, Vol. 10, World Scientific Publ. Co., 2023.

Asymptotic expansions for partitions generated by infinite products (with Walter Bridges, Benjamin Brindle, and Kathrin Bringmann), Math. Ann. (2024). https://doi.org/10.1007/s00208-024-02807-x

Sign changes in statistics for plane partitions (with Walter Bridges and Joshua Males), Journal of Mathematical Analysis and Applications, Volume 530, Issue 1, 2024.

Asymptotics for the twisted eta-product and applications to sign changes in partitions (with Walter Bridges and Taylor Garnowski), Res. Math. Sci. 9, Article Number 61, 2022.

An asymptotic formula for the number of n-dimensional representations of SU(3) (with Kathrin Bringmann), Rev. Mat. Iberoam. 39 (2023), no. 5, 1599–1640.

Dirichlet series with trigonometric coefficients, Integers, Volume 21, Article 23, 2021.

A dominated convergence theorem for Eisenstein series, Annales math Québec, 45, 291–320 2021.

Rational functions, Cotangent sums and Eichler integrals, Research in Number Theory volume 7, Article number: 23, 2021.

Rational functions and Modular forms, Proc. Amer. Math. Soc. 148, 4151–4164, 2020.

Ramanujan identities of higher degree, Research in Number Theory 4, 42, 2018.

Infinite series representations for Dirichlet L-functions at rational arguments, The Ramanujan Journal 46(1): 91–102, 2018.

Contributions to the theory of modular forms and L-functions (PhD Thesis)

Summer 2024: Elliptische Kurven.

Winter 2023/24: Analytische Zahlentheorie 2.

Summer 2023: Analytische Zahlentheorie.

Winter 2022/23: Algebra.

Summer 2022: Elementare Zahlentheorie.

Winter 2021/22: Algebra.

Summer 2021: Seminar Elliptische Funktionen

Fall 2020: Lineare Algebra 1

Summer 2020: Analytische Zahlentheorie

Summer 2018: Modulformen 1

Winter 2017/18: Elementare Zahlentheorie

Winter 2017/18: Funktionentheorie 2

Summer 2017: Funktionentheorie 1