On Drinfeld modular forms of higher rank and quasi-periodic functions

Chen, Yen-Tsung; Gezmiş, Oğuz

doi:10.1090/tran/8547

2021

DOI: 10.1090/tran/8547

|View full text |Cite

Preprint

On Drinfeld modular forms of higher rank and quasi-periodic functions

Yen-Tsung Chen¹,

Oğuz Gezmiş²

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Drinfeld Modular Forms of Arbitrary Rank

Basson,

Breuer,

Pink

2024

Memoirs of the AMS

View full text Add to dashboard Cite

This monograph provides a foundation for the theory of Drinfeld modular forms of arbitrary rank r r and is subdivided into three chapters. In the first chapter, we develop the analytic theory. Most of the work goes into defining and studying the u u -expansion of a weak Drinfeld modular form, whose coefficients are weak Drinfeld modular forms of rank r − 1 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. In the second chapter, we compare the analytic theory with the algebraic one that was begun in a paper of the third author. For any arithmetic congruence subgroup and any integral weight we establish an isomorphism between the space of analytic modular forms with the space of algebraic modular forms defined in terms of the Satake compactification. From this we deduce the important result that this space is finite dimensional. In the third chapter, we construct and study some examples of Drinfeld modular forms. In particular, we define Eisenstein series, as well as the action of Hecke operators upon them, coefficient forms and discriminant forms. In the special case A = F q [ t ] A=\mathbb {F}_q[t] we show that all modular forms for G L r ( Γ ( t ) ) \mathrm {GL}_r(\Gamma (t)) are generated by certain weight one Eisenstein series, and all modular forms for G L r ( A ) \mathrm {GL}_r(A) and S L r ( A ) \mathrm {SL}_r(A) are generated by certain coefficient forms and discriminant forms. We also compute the dimensions of the spaces of such modular forms.

show abstract

Drinfeld Modular Forms of Arbitrary Rank

Basson,

Breuer,

Pink

2024

Memoirs of the AMS

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On Drinfeld modular forms of higher rank and quasi-periodic functions

Cited by 1 publication

References 25 publications

Drinfeld Modular Forms of Arbitrary Rank

Drinfeld Modular Forms of Arbitrary Rank

Contact Info

Product

Resources

About