Dr. Edgar Assing assing@math.uni-bonn.de I am currently interested in analytic problems related to automorphic forms, automorphic representations & L-functions. 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, 11st-15th September 2023.

New perspectives in the analytic theory of automorphic forms, Oxford, 25th-29th September 2023.

Publications and preprints

• On sup-norm bounds part I: ramified Maaß newforms over number fields.
  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.
  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 Borel-Type Congruence subgroups and arithmetic applications.
  ArXiv preprint (2023).

• A note on Sarnak's density hypothesis for Sp(4).
  ArXiv preprint (2023).

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.
• 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).

Miscellaneous

List of Errata