Rational Hauptmoduls are Replicable
Canadian journal of mathematics, Tome 47 (1995) no. 6, pp. 1201-1218

Voir la notice de l'article provenant de la source Cambridge University Press

It is shown that if ƒ is a Hauptmodul with rational integer coefficients for a group G < PGL2(Q)+, of genus zero, containing a with finite index and z ⟼ z+k precisely when k is an integer, then ƒ is replicable. Examples of such functions are given by the Moonshine functions described by Conway and Norton [CN].
DOI : 10.4153/CJM-1995-061-1
Mots-clés : 11F03, 11F22, 30F35
Cummins, C. J.; Norton, S. P. Rational Hauptmoduls are Replicable. Canadian journal of mathematics, Tome 47 (1995) no. 6, pp. 1201-1218. doi: 10.4153/CJM-1995-061-1
@article{10_4153_CJM_1995_061_1,
     author = {Cummins, C. J. and Norton, S. P.},
     title = {Rational {Hauptmoduls} are {Replicable}},
     journal = {Canadian journal of mathematics},
     pages = {1201--1218},
     year = {1995},
     volume = {47},
     number = {6},
     doi = {10.4153/CJM-1995-061-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-061-1/}
}
TY  - JOUR
AU  - Cummins, C. J.
AU  - Norton, S. P.
TI  - Rational Hauptmoduls are Replicable
JO  - Canadian journal of mathematics
PY  - 1995
SP  - 1201
EP  - 1218
VL  - 47
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-061-1/
DO  - 10.4153/CJM-1995-061-1
ID  - 10_4153_CJM_1995_061_1
ER  - 
%0 Journal Article
%A Cummins, C. J.
%A Norton, S. P.
%T Rational Hauptmoduls are Replicable
%J Canadian journal of mathematics
%D 1995
%P 1201-1218
%V 47
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-061-1/
%R 10.4153/CJM-1995-061-1
%F 10_4153_CJM_1995_061_1

[ACMS] Alexander, D., Cummins, C., McKay, J. and Simons, C., Completely replicable functions. In: Groups, Combinatorics and Geometry, Lecture Notes in Math., (ed. Liebeck, M.W. and Saxl, J.), Cambridge Univ. Press, 1992. 87-95 Google Scholar

[ATLAS] Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A. and Wilson, R.A., Atlas of finite groups, Oxford Univ. Press, 1985. Google Scholar

[B1] Borcherds, R.E., Monstrous Moonshine and monstrous Lie super algebras, Invent. Math. 109(1992), 405–444. Google Scholar

[CN] Conway, J.H. and Norton, S.P., Monstrous Moonshine, Bull. London Math. Soc. 11(1979), 308–339. Google Scholar

[F] Ferenbaugh, C.R., On the Modular Functions involved in “Monstrous Moonshine ”, Ph.D. thesis, Princeton University, 1992. Google Scholar

[K] Koike, M., On replication formula and Hecke operators, Nagoya University, preprint. Google Scholar

[N1] Norton, S.P., More on Moonshine. In: Computational Group Theory (éd. Atkinson, M.D.), Academic Press, 1984. 185–193. Google Scholar

[N2] Norton, S.P., Non-monstrous Moonshine, Proceedings of the Columbus conference on the Monster, 1993. to appear. Google Scholar

[Sh] Shimura, G. Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press, 1971. Google Scholar

[Sm] Smith, G.W., Higher genus Moonshine, 1993. preprint. Google Scholar

[T] Thompson, J.G., Some numerology between the Fischer-Griess monster and the elliptic modular function,, Bull. London Math. Soc. 11(1979), 352–353. Google Scholar

Cité par Sources :