Modular-FUN

About

Project title: Modular forms, unitary representations, and numerical methods

Project acronym: Modular-FUN

Project type: institutional research project of the University of Zagreb – Faculty of Geodesy, funded by the European Union – NextGenerationEU through the National Recovery and Resilience Plan 2021–2026

Research field: Mathematics

Duration: 48 months (1 October 2025 – 30 September 2029)

Funding: 59,447.77 EUR

Project summary

The project investigates structural properties of modular and automorphic forms, which are central objects in modern analytic number theory and the Langlands program — a far-reaching collection of conjectures and theories establishing deep connections between number theory, representation theory, and algebraic geometry, thereby creating a conceptual framework that has already led to the solution of numerous important problems, such as the proof of the Modularity Theorem and Fermat’s Last Theorem.

The research focuses on modular and automorphic forms constructed using Poincaré series. One of the main goals is to build on the fundamental principles of the theory of integral non-vanishing criteria for Poincaré series in order to develop new methods for studying various other properties of these series that depend on the local L¹-properties of the inducing functions. The developed methods will be applied to prominent classes of automorphic and modular forms and the associated unitary representations, revealing new information about these important and challenging objects.

Another objective is to develop and implement numerical methods for computing theoretically established constants, leading to new results concerning some of the most well-known families of modular and automorphic forms. Moreover, the project will develop additional numerical and geometric methods, further enriching the approaches employed within the research.

Research Team

Principal investigator

Sonja Žunar Kožić
Assistant Professor
Chair for Mathematics and Physics
University of Zagreb – Faculty of Geodesy

Team members

Iva Kodrnja
Assistant Professor
Chair for Mathematics and Physics
University of Zagreb – Faculty of Geodesy

Ermin Mustafić
Assistant
Chair for Mathematics and Physics
University of Zagreb – Faculty of Geodesy

Nikol Radović
Senior Lecturer
Chair for Mathematics and Physics
University of Zagreb – Faculty of Geodesy

Results

Preprints

Žunar Kožić, S.: A lower bound on the relative L¹-norm of Poincaré series. Preprint (2026)

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Contact

Have any questions or suggestions? Contact us at sonja.zunar@geof.unizg.hr.