Drinfeld modular forms of arbitrary rank, Part I: Analytic Theory

Abstract

This is the first of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank r. In the present part, we develop the analytic theory. Most of the work goes into defining and studying the u-expansion of a weak Drinfeld modular form, whose coefficients are weak Drinfeld modular forms of rank r-1. Based on that we give a precise definition of when a weak Drinfeld modular form is holomorphic at infinity and thus a Drinfeld modular form in the proper sense.

24 pages

References in corpus (2)

• Drinfeld modular forms of arbitrary rank, Part II: Comparison with Algebraic Theory
• Drinfeld modular forms of arbitrary rank, Part III: Examples

Cited by in corpus (4)

• Drinfeld modular forms of arbitrary rank, Part III: Examples
• A product formula for the higher rank Drinfeld discriminant function
• Arithmetic Satake compactifications and algebraic Drinfeld modular forms
• Compactification of Drinfeld Moduli Spaces as Moduli Spaces of $A$-Reciprocal Maps and Consequences for Drinfeld Modular Forms