PARABOLIC GENERALIZED MODULAR FORMS AND THEIR CHARACTERS-Reference-Cited by-同舟云学术

PARABOLIC GENERALIZED MODULAR FORMS AND THEIR CHARACTERS

Published:2009-08 Issue:05 Volume:05 Page:845-857
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

KNOPP MARVIN¹,MASON GEOFFREY²

Affiliation:

1. Department of Mathematics, Temple University, Philadelphia, PA 19122, USA

2. Department of Mathematics, University of California at Santa Cruz, CA 95064, USA

Abstract

We make a detailed study of the generalized modular forms of weight zero and their associated multiplier systems (characters) on an arbitrary subgroup Γ of finite index in the modular group. Among other things, we show that every generalized divisor on the compact Riemann surface associated to Γ is the divisor of a modular form (with unitary character) which is unique up to scalars. This extends a result of Petersson, and has applications to the Eichler cohomology.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042109002419

Reference8 articles.

1. Cohomology of Groups

2. A bounded automorphic form of dimension zero is constant

3. Generalized modular forms

4. On Generalized Modular forms and their Applications

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