Israel Journal of Mathematics

, Volume 165, Issue 1, pp 93–101 | Cite as

Linear relations and congruences for the coefficients of Drinfeld modular forms

Article
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Abstract

We find congruences for the t-expansion coefficients of Drinfeld modular forms for \(GL_2 (\mathbb{F}_q [T])\). We give generalized analogies of Siegel’s classical observation on SL 2(ℤ) by determining all the linear relations among the initial t-expansion coefficients of Drinfeld modular forms for \(GL_2 (\mathbb{F}_q [T])\). As a consequence spaces M k 0 are identified, in which there are congruences for the s-expansion coefficients.

Keywords

Linear Relation Modular Form Eisenstein Series Cusp Form Consequence Space 
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References

  1. [1]
    S. Choi, Congruences for the coefficients of Drinfeld modular forms, Journal of Number Theory, preprint.Google Scholar
  2. [2]
    S. Choi, Some formulas for the coefficients of Drinfeld modular forms, Journal of Number Theory 116 (2006), 159–167.MathSciNetMATHGoogle Scholar
  3. [3]
    Y. Choie, W. Kohnen and K. Ono, Linear relations between modular form coefficients and non-ordinary primes, The Bulletin of the London Mathematical Society 37 (2005), 335–341.CrossRefMathSciNetMATHGoogle Scholar
  4. [4]
    J. Gallardo and B. Lopez, “Weak” congruences for coefficients of the Eisenstein series for \(\mathbb{F}_q [T]\) of weight q k − 1, Journal of Number Theory 102 (2003), 107–117.CrossRefMathSciNetMATHGoogle Scholar
  5. [5]
    E. U. Gekeler, Finite modular forms, Finite Fields and their Applications 7 (2001), 553–572.CrossRefMathSciNetMATHGoogle Scholar
  6. [6]
    E. U. Gekeler, Growth order and congruences of coefficients of the Drinfeld discriminant function, Journal of Number Theory 77 (1999), 314–325.CrossRefMathSciNetMATHGoogle Scholar
  7. [7]
    E. U. Gekeler, On the coefficients of Drinfeld modular forms, Inventiones Mathematicae 93 (1988), 667–700.CrossRefMathSciNetMATHGoogle Scholar
  8. [8]
    K. Hatada, Eigenvalues of Hecke operators on SL(2, Z), Mathematische Annalen 239 (1979), 75–96.CrossRefMathSciNetMATHGoogle Scholar
  9. [9]
    B. López, A congruence for the coefficients of the Drinfeld discriminant function, C. R. Acad. Sci. Paris Ser. I Math. 330 (2000), 1053–1058.MathSciNetMATHGoogle Scholar
  10. [10]
    C. L. Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, (German) Nachrichten der Akademie der Wissenschaften in Gottingen. II. (1969), 87–102.Google Scholar

Copyright information

© The Hebrew University of Jerusalem 2008

Authors and Affiliations

  1. 1.Department of Mathematics EducationDongguk UniversityKyongjuRepublic of Korea

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