EICHLER COHOMOLOGY THEOREM FOR GENERALIZED MODULAR FORMS

2011 ◽  
Vol 07 (04) ◽  
pp. 1103-1113 ◽  
Author(s):  
WISSAM RAJI
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Large Integer ◽  
Isomorphism Theorem ◽  
Classical Approach ◽  
Negative Weight ◽  
Eichler Cohomology ◽  
Automorphic Integrals

We show starting with relations between Fourier coefficients of weakly parabolic generalized modular forms of negative weight that we can construct automorphic integrals for large integer weights. We finally prove an Eichler isomorphism theorem for weakly parabolic generalized modular forms using the classical approach as in [3].

EICHLER COHOMOLOGY THEOREM FOR VECTOR-VALUED MODULAR FORMS

2013 ◽  
Vol 09 (07) ◽  
pp. 1765-1788 ◽  
Author(s):  
JOSE GIMENEZ
Keyword(s):  
Modular Forms ◽  
Modular Group ◽  
Large Integer ◽  
Eichler Cohomology ◽  
Vector Valued

We prove the Eichler cohomology theorem for vector-valued modular forms of large integer weights on the full modular group.

FOURIER COEFFICIENTS OF GENERALIZED MODULAR FORMS OF NEGATIVE WEIGHT

2009 ◽  
Vol 05 (01) ◽  
pp. 153-160 ◽  
Author(s):  
WISSAM RAJI
Keyword(s):  
Modular Forms ◽  
Modular Group ◽  
Fourier Coefficients ◽  
Circle Method ◽  
Negative Weight

The Fourier coefficients of classical modular forms of negative weights have been determined for the case for which F(τ) belongs to a subgroup of the full modular group [9]. In this paper, we determine the Fourier coefficients of generalized modular forms of negative weights using the circle method.

ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS

2010 ◽  
Vol 06 (01) ◽  
pp. 69-87 ◽  
Author(s):  
ALISON MILLER ◽  
AARON PIXTON
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Algebraic Numbers ◽  
Heegner Points ◽  
Positive Weight ◽  
Poincare Series ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Modular Invariants

We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic away from the cusp at infinity, then the traces of values at Heegner points of a certain iterated non-holomorphic derivative of f are equal to Fourier coefficients of the half-integral weight modular forms [Formula: see text].

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 On mod p singular modular forms

2016 ◽  
Vol 28 (6) ◽  
Author(s):  
Siegfried Böcherer ◽  
Toshiyuki Kikuta
Keyword(s):  
Modular Form ◽  
Number Field ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Siegel Modular Form ◽  
Mod P

AbstractWe show that a Siegel modular form with integral Fourier coefficients in a number field

INDEX-DEPENDENT DIVISORS OF COEFFICIENTS OF MODULAR FORMS

2013 ◽  
Vol 09 (07) ◽  
pp. 1841-1853 ◽  
Author(s):  
B. K. MORIYA ◽  
C. J. SMYTH
Keyword(s):  
Prime Number ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Survey Methods ◽  
Integer Sequences ◽  
Positive Integers

We evaluate [Formula: see text] for a certain family of integer sequences, which include the Fourier coefficients of some modular forms. In particular, we compute [Formula: see text] for all positive integers n for Ramanujan's τ-function. As a consequence, we obtain many congruences — for instance that τ(1000m) is always divisible by 64000. We also determine, for a given prime number p, the set of n for which τ(pn-1) is divisible by n. Further, we give a description of the set {n ∈ ℕ : n divides τ(n)}. We also survey methods for computing τ(n). Finally, we find the least n for which τ(n) is prime, complementing a result of D. H. Lehmer, who found the least n for which |τ(n)| is prime.

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