Dr. Edgar Assing
I am currently interested in analytic problems related to automorphic forms, automorphic representations & Lfunctions. In particular I am exploring how the language of automorphic representations can unravel new features that (for me) remain somehow mystical from the classical point of view.


Upcoming talks and travel
Dynamics and asymptotic in algebra and number theory, Bielefeld, 11st15th September 2023.
New perspectives in the analytic theory of automorphic forms, Oxford, 25th29th September 2023.
Publications and preprints

On supnorm bounds part I: ramified Maaß newforms over number fields.
ArXiv preprint (2017).

On the size of padic Whittaker functions.
Trans. Amer. Math. Soc. (2018), DOI:
10.1090/tran/7685.
ArXiv preprint (2018).

Adelic Voronoi Summation and Subconvexity for GL(2) LFunctions in the depth Aspect.
International Journal of Number Theory (2021), DOI:
10.1142/S1793042121500470.
ArXiv preprint (2018). Original title: Yet another GL_{2} subconvexity result.

Voronoi summation for halfintegral weight automorphic forms (with A. Corbett).
International Mathematics Research Notices (2021), DOI: rnab238.
ArXiv preprint (2020).

The supnorm problem beyond the newform.
ArXiv preprint (2021).

The density conjecture for principal congruence subgroups (with V. Blomer).
Duke Math. J. (to appear).
ArXiv preprint (2022).

A density theorem for BorelType Congruence subgroups and arithmetic applications.
ArXiv preprint (2023).

A note on Sarnak's density hypothesis for Sp(4).
ArXiv preprint (2023).
Doctoral Thesis
I did my PhD at the University of Bristol mainly thinking about supnorms of automorphic forms and related topics. The outcome was the following thesis.

Local Analysis of Whittaker New Vectors and Global Applications
[PDF].
Teaching
Teaching duties at the University of Bonn (From 1.10.2019):

WS19/20: Assistent der Vorlesung Lineare Algebra 1 gehalten von Prof. Dr. M. Lesch.

SS20: Selected topics in Algebra  Topics in Automorphic Forms.

SS20: Assistent for the Graduate Seminar on Advanced Number Theory.

WS20/21: Selected topics in Analysis  Topics in Analytic Number Theory.

WS20/21: Assistent for the lecture Advanced Algebra 1  Liealgebren und Darstellungen.

SS21: Graduate Seminar on Advanced Number Theory  Modular Forms and Applications (together with Asbjørn Nordentoft).

SS21: Assistent der Vorlesung Algebra 1 gehalten von Prof. Dr. J. Franke.

WS21/22: Selected Topics in Number Theory  The Circle Method and Waring's problem.

WS21/22: Assistent der Vorlesung Einführung in die Algebra gehalten von Prof. Dr. V. Blomer.

SS22: Selected Topics in Number Theory  Thin Groups and Applications.

SS22: Assistent der Vorlesung Algebra 1 gehalten von Prof. Dr. V. Blomer.

WS22/23: Algebra 2 (Class Field Theory).

SS23: Advanced Algebra 1 (Modular Forms).

WS23/24: Selected Topics in Analysis and PDE (Arithmetic Quantum Chaos).
Supervised Students:

S. Romano (Integral Points On Rosenberger Type Surfaces, Master's thesis 2022).

A. Acosta Reche (Weyl's Law for Cocompact Lattices Arising from Quaternion Algebras, Master's thesis 2023).

M. Kristen (Supnorms over function fields, Master's thesis in progress).

F. Hinrichs (Über mögliche Erweiterungen von Hecke's Umkehrsatz, Bachelor's thesis 2023).

D. Wendler (On class field towers, Bachelor's thesis 2023).

L. Karras (On bounds for Ihara's constant, Bachelor's thesis 2023).
Miscellaneous
This is a recording of my online talk in the Budapest Automorphic Form Seminar (25. November 2021).
This is a short note on a certain integral identity involving Gegenbauer Polynomials and the IBessel function.
List of Errata
Here is an
errata sheet for my published papers. Note that ArXiv versions might differ from published versions in several aspects!