LINEAR RELATIONS FOR COEFFICIENTS OF DRINFELD MODULAR FORMS

2008 ◽  
Vol 04 (02) ◽  
pp. 171-176
Author(s):  
MATIJA KAZALICKI
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Linear Relations ◽  
Drinfeld Modular Forms ◽  
Divisibility Properties

Choie, Kohnen and Ono have recently classified the linear relations among the initial Fourier coefficients of weight k modular forms on SL2(ℤ), and they employed these results to obtain particular p-divisibility properties of some p-power Fourier coefficients that are common to all modular forms of certain weights. Using this, they reproduced some famous results of Hida on non-ordinary primes. Here we generalize these results to Drinfeld modular forms.

scholarly journals Restriction of Siegel modular forms to modular curves

2002 ◽  
Vol 65 (2) ◽  
pp. 239-252 ◽  
Author(s):  
Cris Poor ◽  
David S. Yuen
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Congruence Subgroup ◽  
Siegel Modular Forms ◽  
Siegel Modular Form ◽  
Modular Curves ◽  
Linear Relations

We study homomorphisms form the ring of Siegel modular forms of a given degree to the ring of elliptic modular forms for a congruence subgroup. These homomorphisms essentially arise from the restriction of Siegel modular forms to modular curves. These homomorphisms give rise to linear relations among the Fourier coefficients of a Siegel modular form. We use this technique to prove that dim .

scholarly journals Linear relations between modular forms for Г0+(p)

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
SoYoung Choi ◽  
Chang Heon Kim
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Linear Relations

AbstractWe find linear relations among the Fourier coefficients of modular forms for the group Г

scholarly journals Divisibility properties for weakly holomorphic modular forms with sign vectors

2016 ◽  
Vol 12 (08) ◽  
pp. 2107-2123 ◽  
Author(s):  
Yichao Zhang
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Hecke Operators ◽  
Orthogonal Direction ◽  
Weakly Holomorphic Modular Forms ◽  
Divisibility Properties ◽  
Holomorphic Modular Forms

In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms with sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight [Formula: see text], which is related to the weight of Borcherds lifts when [Formula: see text]. In particular, we see that such divisibility of the weight of Borcherds lifts only exists for [Formula: see text]. By considering Hecke operators for the spaces of weakly holomorphic modular forms with sign vectors, we obtain divisibility results in an “orthogonal” direction on reduced modular forms.

scholarly journals Linear relations between Fourier coefficients of special Siegel modular forms

2004 ◽  
Vol 173 ◽  
pp. 153-161 ◽  
Author(s):  
Winfried Kohnen
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Siegel Modular Forms ◽  
Linear Relations

AbstractIn this paper we give certain linear relations between the Fourier coefficients of Siegel modular forms that are obtained from Ikeda lifts.

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

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