Dr. Edgar Assing assing@math.uni-bonn.de I am currently interested in analytic problems related to automorphic forms, automorphic representations & L-functions. More precisley, I am working at the interface between analytic number theory, automorphic forms and (local and global) representation theory.

Upcoming talks and travel

Publications and preprints

• On sup-norm bounds part I: ramified Maaß newforms over number fields.
  J. Eur. Math. Soc. (Online first, 2024 ), DOI: 10.4171/JEMS/1444.
  ArXiv preprint (2017).

• On sup-norm bounds part II: GL(2) Eisenstein series.
  Forum Mathematicum (2019), DOI: 10.1515/forum-2018-0014.
  ArXiv preprint (2018).

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

• Adelic Voronoi Summation and Subconvexity for GL(2) L-Functions in the depth Aspect.
  International Journal of Number Theory (2021), DOI: 10.1142/S1793042121500470.
  ArXiv preprint (2018). Original title: Yet another GL₂ subconvexity result.

• Voronoi summation via switching cusps (with A. Corbett).
  Monatsh Math (2021), DOI: 10.1007/s00605-021-01537-5.
  ArXiv preprint (2019).

• Uniform Titchmarsh divisor problems (with V. Blomer and Junxian Li).
  Adv. Math. (2021), DOI:10.1016/j.aim.2021.108076.
  ArXiv preprint (2020).

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

• The sup-norm problem beyond the newform.
  Math. Proc. Cambridge Philos. Soc. (2024), DOI: 10.1017/S0305004124000021.
  ArXiv preprint (2021).

• The density conjecture for principal congruence subgroups (with V. Blomer).
  Duke Math. J. (2024), DOI: 10.1215/00127094-2023-0040.
  ArXiv preprint (2022).

• A density theorem for Borel-Type Congruence subgroups and arithmetic applications.
  ArXiv preprint (2023).

• A note on Sarnak's density hypothesis for Sp(4).
  Comm. Math. Helv. (to appear).
  ArXiv preprint (2023).

• An observation concerning highly ramified ε-factors.
  Rocky Mountain J. Math. (to appear).
  ArXiv preprint (2024).

• Local analysis of the Kuznetsov formula and the density conjecture (with V. Blomer and Paul D. Nelson).
  ArXiv preprint (2024).

• New bounds for fundamental Fourier coefficients of Siegel modular forms.
  ArXiv preprint (2024).

• Unipotent mixing for general moduli.
  ArXiv preprint (2024).

Doctoral Thesis

• Local Analysis of Whittaker New Vectors and Global Applications [PDF].

Teaching

• WS19/20: Assistent der Vorlesung Lineare Algebra 1 gehalten von Prof. Dr. M. Lesch.
• SS20: Selected topics in Algebra - Topics in Automorphic Forms. [Script]
• SS20: Assistent for the Graduate Seminar on Advanced Number Theory.
• WS20/21: Selected topics in Analysis - Topics in Analytic Number Theory. [Script]
• 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. [Script]
• 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. [Script]
• SS22: Assistent der Vorlesung Algebra 1 gehalten von Prof. Dr. V. Blomer.
• WS22/23: Algebra 2 (Class Field Theory). [Script]
• SS23: Advanced Algebra 1 (Modular Forms). [Script]
• WS23/24: Selected Topics in Analysis and PDE (Arithmetic Quantum Chaos). [Script]
• WS23/24: Assistent for the lecture Algebraic Number Theory by Prof. Dr. G. Dill.
• SS24: Selected Topics in Number Theory (On gaps between primes). [Script]
• SS24: Proseminar S1G1 (together with Koen van den Dungen).
• WS24/25: Advanced Topics in Analysis (Selberg trace formula).
• SS25: Proseminar S1G1 (Kreis und Kugel).

Miscellaneous

List of Errata