Manuscripta Mathematica

, Volume 144, Issue 3–4, pp 503–515 | Cite as

The zeros of certain weakly holomorphic Drinfeld modular forms

  • SoYoung Choi
  • Bo-Hae ImEmail author


Duke and Jenkins (Pure Appl Math Q 4(4):1327–1340, 2008) constructed a canonical basis for the space of weakly holomorphic modular forms for \({{\rm SL}_2(\mathbb{Z})}\) and investigated the zeros of the basis elements. In this paper we give an analogy in the Drinfeld setting of the result given by Duke and Jenkins (Pure Appl Math Q 4(4):1327–1340, 2008).

Mathematics Subject Classification (2000)

Primary 11F03 11F11 Secondary 11F37 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Choi, S.: On the Coefficients of Weakly Holomorphic Drinfeld Modular Forms, submitted (2012)Google Scholar
  2. 2.
    Choi S.: Some formulas for the coefficients of Drinfeld modular forms. J. Number Theory 116(1), 159–167 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Cornelissen G.: Sur les zeros des series d’Eisenstein de poids q k−1 pour \({{\rm GL}_2 (\mathbb{F}_q [T])}\). C. R. Acad. Sci. Paris Ser. I Math. 321(7), 817–820 (1995)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Cornelissen, G.: Geometric Properties of Modular Forms over Rational Function Fields. Ph.D. thesis. University of Gent (1997)Google Scholar
  5. 5.
    Duke W., Jenkins P.: On the zeros and coefficients of certain weakly holomorphic modular forms. Pure Appl. Math. Q. 4(4), 1327–1340 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Gekeler E.U.: A product expansion for the discriminant function of Drinfeld modules of rank two. J. Number Theory 21(2), 135–140 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Gekeler E.U.: On the coefficients of Drinfeld modular forms. Invent. Math. 93(3), 667–700 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gekeler E.U.: On the Drinfeld discriminant function. Compos. Math. 106(2), 181–202 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Gekeler E.U.: Zero distribution and decay at infinity of Drinfeld modular coefficient forms. Int. J. Number Theory 7(3), 671–693 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Kazalicki M.: Zeros of certain Drinfeld modular functions. J. Number Theory 128(6), 1662–1669 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Koblitz, N.: p-adic numbers, p-adic analysis, and zeta-functions, GTM 58 (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics EducationDongguk University-GyeongjuGyeongjuSouth Korea
  2. 2.Department of MathematicsChung-Ang UniversitySeoulSouth Korea

Personalised recommendations