Super-replicable functions ${\cal N}(j_{1,N})$ and periodically vanishing property

참고문헌 (Reference)

1 "The q-series of monstrous moonshine and the decompositionof the head characters" -18, 1990

2 Duke Math, "The genus-zero problem for njh-type groups" 1993

3 N. Ishida, "The equation for the modular curve X 1 derived from theequation for the modular curve X" 22 (22): 167-175, 1999

4 C. H. Kim, "Self-recursion formulas satised by Fourier coecients of some modular functions" 160 (160): 53-65, 2001

5 C. H. Kim, "Self-recursion formulas of certain monstrous functions" 171 (171): 27-40, 2002

6 C. R. Ferenbaugh, "Replication formulae for njh-type Hauptmoduls" 179 (179): 808-837, 1996

7 C. J. Cummins, "Rational Hauptmoduls are replicable" 47 (47): 1201-1218, 1995

8 C. H. Kim, "On the genus of some modular curve of level N" 54 (54): 291-297, 1996

9 "On modular forms of half integral weight" 1973

10 "More on moonshine" Academic Press 1984185{193

11 "Introduction to the Arithmetic Theory of Automorphic Functions" Prince-ton Univ Press 1971

12 "Introduction to Elliptic Curves and Modular Forms" Springer-Verlag 1984

13 Lang, "Graduate Texts in Mathematics" Springer-Verlag 1987

14 S. J. Kang, "Graded Lie superalgebras, supertrace formula, and orbit Liesuperalgrbra" 81 (81): 675-724, 2000

15 S. J. Kang, "Graded Lie superalgebras and the superdimension formula" 204 (204): 597-655, 1998

16 S. J. Kang, "Graded Lie superalgebras and super-replicable functions" 285 (285): 531-573, 2005

17 "Good reduction of abelian varieties" 1968

18 "Generators of function elds of the moldular curves X 1"

19 K. J. Hong, "Generation of class elds by the modular function j 1;12" 93 (93): 257-291, 2000

20 "Generation of Hauptmoduln of 1" -1,

21 C. H. Kim, "Arithmetic of the modular function j 1;8" 4 (4): 317-338, 2000

22 "Advanced Topics in the Arithmetic of Elliptic Curves" Springer-Verlag 1994

23 I, "A natural representation of the Fischer-Griess monster with the modular function J as character" 1984