Mathematische Annalen

, Volume 327, Issue 2, pp 293–303

The arithmetic of Borcherds' exponents

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References

  1. 1.
    Borcherds, R.E.: Automorphic forms on O s+2,2(ℝ) and infinite products. Invent. Math. 120, 161–213 (1995)MathSciNetMATHGoogle Scholar
  2. 2.
    Cox, D.:Primes of the form x 2+ny 2, Fermat, Class Field Theory, and Complex Multiplication. Wiley Publ., New York, 1989Google Scholar
  3. 3.
    Deuring, M.: Teilbarkeitseigenschaften der singulären moduln der elliptischen funktionen und die diskriminante der klassengleichung. Comm. Math. Helv. 19, 74–82 (1946)MathSciNetMATHGoogle Scholar
  4. 4.
    Gross, B., Zagier, D.: On singular moduli. J. reine angew. math. 355, 191–220 (1985)MathSciNetMATHGoogle Scholar
  5. 5.
    Ireland, K., Rosen, M.: A classical introduction to modern number theory. Springer- Verlag, New York, 1990Google Scholar
  6. 6.
    Kaneko, M., Zagier, D.: Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials Comp. perspectives on Number Theory (Chicago, Illinois 1995). AMS/IP Stud. Adv. Math. Amer. Math. Soc. 7, 97–126 (1998)Google Scholar
  7. 7.
    Lang, S.: Elliptic functions. 2nd edition Springer-Verlag, 1987Google Scholar
  8. 8.
    Ogg, A.: Survey of modular functions of one variable. Springer Lect. Notes in Math. 320, 1–36 (1973)MATHGoogle Scholar
  9. 9.
    Serre, J.-P.: Congruences et formes modulaires (d'après H. P. F. Swinnerton-Dyer). Sem. Bourbaki 416(1971–1972), 74–88Google Scholar
  10. 10.
    Serre, J.-P.: Formes modulaires et fonctions zêta p-adiques. Springer Lect. Notes in Math. 350, 191–268 (1973)MATHGoogle Scholar
  11. 11.
    Shimura, G.: Introduction to the arithmetic of automorphic forms. Iwanawi Shoten and Princeton Univ. Press, 1971Google Scholar

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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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