p-Adic Properties of Values of the Modular j-Function

  • Ken Ono
  • Matthew A. Papanikolas
Part of the Developments in Mathematics book series (DEVM, volume 11)


As usual, let q:=e2πizand letj(z) be the classical modular function
$$ j(z) = \sum\limits_{n = - 1}^\infty {c(n){q^n} = {q^{ - 1}} + 744 + 196884q + \cdot \cdot \cdot } $$


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [A-K-N]
    T. Asai, M. Kaneko and H. Ninomiya, Zeros of certain modular functions and an application, Comm. Math. Univ. St. Pauli 46 (1997) 93–101.MathSciNetMATHGoogle Scholar
  2. [B-K-O]
    J. Bruinier, W. Kohnen and K. Ono, The arithmetic of the values of modular functions and the divisors of modular forms,Compositio Mathematica, accepted for publication.Google Scholar
  3. [G-Z]
    B. Gross and D. Zagier, On singular moduli, J. reine angew. math. 355 (1985) 191–220.MathSciNetMATHGoogle Scholar
  4. [K]
    M. Kaneko, Traces of singular moduli and the Fourier coefficients of the elliptic modular function j(r),in “Number theory (Ottawa, ON, 1996),” 173–176, CRM Proc. and Lecture Notes, 19. Amer. Math. Soc., Providence, RI, 1999.Google Scholar
  5. [Se]
    J.-P. Serre, Formes modulaires et fonctions zêta p-adiques, in “Modular functions of one variable. III (Willem Kuyk and J.-P. Serre, ed.),” 191268, Lecture Notes in Mathematics, 350. Springer-Verlag, Berlin-New York, 1973.Google Scholar
  6. [Si]
    J. H. Silverman, “Advanced Topics in the Arithmetic of Elliptic Curves,”Springer-Verlag, New York, 1994.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ken Ono
    • 1
  • Matthew A. Papanikolas
    • 2
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

Personalised recommendations