Geodesic
On Functions Satisfying Modular Equations for Infinitely Many Primes
Canadian journal of mathematics, Tome 51 (1999) no. 5, pp. 1020-1034

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

In this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are: 1) every such function is analytic in the upper half plane; 2) if such function takes the same value in two different points ${{z}_{1}}$ and ${{z}_{2}}$ then there exists an $f$ -preserving analytic bijection between neighbourhoods of ${{z}_{1}}$ and ${{z}_{2}}$ .
DOI : 10.4153/CJM-1999-045-x
Mots-clés : 11Mxx 
Kozlov, Dmitry N. On Functions Satisfying Modular Equations for Infinitely Many Primes. Canadian journal of mathematics, Tome 51 (1999) no. 5, pp. 1020-1034. doi: 10.4153/CJM-1999-045-x
@article{10_4153_CJM_1999_045_x,
     author = {Kozlov, Dmitry N.},
     title = {On {Functions} {Satisfying} {Modular} {Equations} for {Infinitely} {Many} {Primes}},
     journal = {Canadian journal of mathematics},
     pages = {1020--1034},
     year = {1999},
     volume = {51},
     number = {5},
     doi = {10.4153/CJM-1999-045-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1999-045-x/}
}
TY  - JOUR
AU  - Kozlov, Dmitry N.
TI  - On Functions Satisfying Modular Equations for Infinitely Many Primes
JO  - Canadian journal of mathematics
PY  - 1999
SP  - 1020
EP  - 1034
VL  - 51
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1999-045-x/
DO  - 10.4153/CJM-1999-045-x
ID  - 10_4153_CJM_1999_045_x
ER  - 
%0 Journal Article
%A Kozlov, Dmitry N.
%T On Functions Satisfying Modular Equations for Infinitely Many Primes
%J Canadian journal of mathematics
%D 1999
%P 1020-1034
%V 51
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1999-045-x/
%R 10.4153/CJM-1999-045-x
%F 10_4153_CJM_1999_045_x

[1] [1] Alexander, D., Cummins, C., McKay, J. and Simons, C., Completely replicable functions. In: Groups, combinatorics and geometry (Durham, 1990), Cambridge Univ. Press, Cambridge, 1992, 87–98. Google Scholar

[2] [2] Borcherds, R. E., Monstrous moonshine and monstrous Lie superalgebras. Invent.Math. 109(1992), 405–444. Google Scholar

[3] [3] Borcherds, R. E. and Ryba, A. J. E., Modular Moonshine II. Duke Math. J. 83(1996), 435–459. Google Scholar

[4] [4] Cohn, H. and McKay, J., Spontaneous generation of modular invariants. Math. Comp. 65(1996), 1295–1309. Google Scholar

[5] [5] Cohn, H. and McKay, J., Modular functions from nothing. Preprint, 1994. Google Scholar

[6] [6] Conway, J. H. and Norton, S. P., Monstrous moonshine. Bull. LondonMath. Soc. 11(1979), 308–339. Google Scholar

[7] [7] Cummins, C. J. and Gannon, T., Modular equations and the genus zero property of moonshine functions. Invent. Math. (3) 129(1998), 413–443. Google Scholar

[8] [8] Frenkel, I. B., Lepowsky, J. and Meurman, A., Vertex operators and theMonster. Academic Press, Boston, 1988. Google Scholar

[9] [9] Mahler, K., On a class of non-linear functional equations connected with modular functions. J. Austral. Math. Soc. 22(A)(1976), 65–118. Google Scholar

[10] [10] Martin, Y., On modular invariance of completely replicable functions. In: Moonshine, theMonster, and related topics (South Hadley, MA, 1994), Contemp.Math. 193(1996), 263–286. Google Scholar

[11] [11] McKay, J. and Strauss, H., The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18(1990), 253–278. Google Scholar

[12] [12] Norton, S. P., More on moonshine. In: Computational Group Theory (ed. Atkinson, M. D.), Academic Press, 1984, 185–193. Google Scholar

[13] [13] Norton, S. P., Non-monstrous Moonshine. In: “Groups, Difference Sets, and theMonster” (eds. Arasu, K. T. et al.), de Gruyter, 1996, 433–441. Google Scholar

Cité par Sources :