On generalized modular forms supported on cuspidal and elliptic points

Suppose  N ∈{13,17,19,21,26,29,31,34,39,41,49,50}. In this paper, we extend previous results of Kohnen–Mason (On the canonical decomposition of generalized modular functions, 2010 ) to prove that generalized modular forms for  Γ 0 ( N ) with rational Fourier expansions whose divisors are supported o...

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Bibliographic Details
Published in:The Ramanujan journal 2012-04, Vol.27 (3), p.285-295
Main Authors: Kilford, L. J. P., Raji, Wissam
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Summary:Suppose  N ∈{13,17,19,21,26,29,31,34,39,41,49,50}. In this paper, we extend previous results of Kohnen–Mason (On the canonical decomposition of generalized modular functions, 2010 ) to prove that generalized modular forms for  Γ 0 ( N ) with rational Fourier expansions whose divisors are supported only at the cusps and at the elliptic points are actually classical modular forms. We discuss possible limitations to this extension and pose questions about possible zeroes for modular forms of prime level.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-011-9344-8