From the Carlitz exponential to Drinfeld modular forms

2019/10/01 by Federico Pellarin, Pellarin, Federico
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.00322

openalex publication_date 2019/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper contains the written notes of a course the author gave at the VIASM of Hanoi in the Summer 2018. It provides an elementary introduction to the analytic naive theory of Drinfeld modular forms for the simplest 'Drinfeld modular group' GL 2 (Fq[θ]) also providing some perspectives of development, notably in the direction of the theory of vector modular forms with values in certain ultrametric Banach algebras.

Related

• Drinfeld modular forms of arbitrary rank, Part I: Analytic Theory
• The analytic theory of vectorial Drinfeld modular forms
• Drinfeld modular forms of arbitrary rank, Part III: Examples
• Drinfeld modular forms of arbitrary rank, Part II: Comparison with Algebraic Theory
• The Geometry of Drinfeld Modular Forms