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1998 | 84 | 2 | 129-143
Tytuł artykułu

Arithmetic of the modular function $j_{1,4}$

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EN
Abstrakty
EN
We find a generator $j_{1,4}$ of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator $N(j_{1,4})$ which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Słowa kluczowe
Twórcy
  • Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
autor
  • Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
Bibliografia
  • [1] Borcherds, R.E., Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109 (1992), 405-444.
  • [2] Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., and Wilson, R.A., Atlas of Finite Groups, Clarendon Press, 1985.
  • [3] Conway, J.H. and Norton, S.P., Monstrous moonshine, Bull. London Math. Soc. 11 (1979), 308-339.
  • [4] Deuring, M., Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg 14 (1941), 197-272.
  • [5] Foster, O., Lectures on Riemann Surfaces, Springer, 1981.
  • [6] Frenkel, I.B., Lepowsky, J., and Meurman, A., Vertex Operator Algebras and the Monster, Academic Press, Boston, 1988.
  • [7] Frenkel, I.B., Lepowsky, J., and Meurman, A., A natural representation of the Fischer-Griess monster with the modular function J as character, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), 3256-3260.
  • [8] Kim, C.H. and Koo, J.K., On the modular function j₄ of level 4, preprint.
  • [9] Kim, C.H. and Koo, J.K., On the genus of some modular curve of level N, Bull. Austral. Math. Soc. 54 (1996), 291-297.
  • [10] Kim, C.H. and Koo, J.K., On the modular function $j_{1,2}$, in preparation.
  • [11] Koike, M., On replication formula and Hecke operators, preprint, Nagoya University.
  • [12] Lang, S., Algebra, Addison-Wesley, 1993.
  • [13] Lang, S.,, Elliptic Functions, Springer, 1987.
  • [14] Néron, A., Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. I.H.E.S. 21 (1964), 5-128.
  • [15] Norton, S.P., More on moonshine, in: Computational Group Theory, Academic Press, London, 1984, 185-195.
  • [16] Rankin, R., Modular Forms and Functions, Cambridge Univ. Press, Cambridge, 1977.
  • [17] Schoeneberg, B., Elliptic Modular Functions, Springer, 1973.
  • [18] Serre, J.-P. and Tate, J., Good reduction of abelian varieties, Ann. of Math. 88 (1968), 492-517.
  • [19] Shimura, G., Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan 11, Tokyo, 1971.
  • [20] Thompson, J.G., Some numerology between the Fischer-Griess monster and the elliptic modular function, Bull. London Math. Soc. 11 (1979), 352-353.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-aav84i2p129bwm
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