scholarly journals Zeros of weakly holomorphic modular forms of levels 2 and 3

2013 ◽  
Vol 20 (4) ◽  
pp. 657-674 ◽  
Author(s):  
Sharon Anne Garthwaite ◽  
Paul Jenkins
Keyword(s):  
Modular Forms ◽  
Weakly Holomorphic Modular Forms ◽  
Holomorphic Modular Forms

scholarly journals On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

2019 ◽  
Vol 17 (1) ◽  
pp. 1631-1651
Author(s):  
Ick Sun Eum ◽  
Ho Yun Jung
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Singular Values ◽  
Congruence Subgroups ◽  
Maass Form ◽  
Weakly Holomorphic Modular Forms ◽  
Reciprocity Law ◽  
Class Invariants ◽  
Higher Genus ◽  
Holomorphic Modular Forms

Abstract After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the Fourier coefficients of weakly holomorphic modular forms of weight 3/2 on the congruence subgroups of higher genus by using the Bruinier-Funke modular traces. Extending their work, we construct real-valued class invariants by using the singular values of the generalized Weber functions of level 5 and prove that their Galois traces are Fourier coefficients of a harmonic weak Maass form of weight 3/2 by using Shimura’s reciprocity law.

scholarly journals Rank generating functions as weakly holomorphic modular forms

2008 ◽  
Vol 133 (3) ◽  
pp. 267-279 ◽  
Author(s):  
Scott Ahlgren ◽  
Stephanie Treneer
Keyword(s):  
Modular Forms ◽  
Generating Functions ◽  
Weakly Holomorphic Modular Forms ◽  
Holomorphic Modular Forms
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