|
On congruences of Jacobi forms
Author(s):
Olav
K.
Richter
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2729-2734.
MSC (2000):
Primary 11F50;
Secondary 11F60
Posted:
April 15, 2008
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We consider congruences and filtrations of Jacobi forms. More specifically, we extend Tate's theory of theta cycles to Jacobi forms, which allows us to prove a criterion for an analog of Atkin's  -operator applied to a Jacobi form to be nonzero modulo a prime.
References:
-
- 1.
- S. Ahlgren and K. Ono, Arithmetic of singular moduli and class polynomials, Compos. Math. 141 (2005), no. 2, 293-312. MR 2134268 (2006a:11058)
- 2.
- M. Chida and M. Kaneko, On ordinary primes for modular forms and the theta operator, Proc. Amer. Math. Soc. 135 (2007), no. 4, 1001-1005. MR 2262900
- 3.
- Y. Choie and W. Eholzer, Jacobi forms and generalized RC-algebras, Rocky Mountain J. Math. 31 (2001), no. 4, 1265-1275. MR 1895295 (2003d:11072)
- 4.
- M. Eichler and D. Zagier, The theory of Jacobi forms, Birkhäuser, Boston, 1985. MR 781735 (86j:11043)
- 5.
- N. Elkies, K. Ono, and T. Yang, Reduction of CM elliptic curves and modular function congruences, Internat. Math. Res. Notices 2005, no. 44, 2695-2707. MR 2181309 (2006k:11076)
- 6.
- P. Guerzhoy, On
 -congruences, Proc. Amer. Math. Soc. 135 (2007), no. 9, 2743-2746. MR 2317947 - 7.
- N. Jochnowitz, A study of the local components of the Hecke algebra mod
 , Trans. Amer. Math. Soc. 270 (1982), no. 1, 253-267. MR 642340 (83e:10033a) - 8.
- M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms, in: The moduli space of curves (Texel Island, 1994), Progr. Math. 129, pp. 165-172, Birkhäuser, Boston, 1995. MR 1363056 (96m:11030)
- 9.
- T. Kawai and K. Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000), no. 2, 397-485. MR 1838446 (2002g:11054)
- 10.
- K. Ono, The web of modularity: Arithmetic of the coefficients of modular forms and
 -series, CBMS Regional Conference Series in Mathematics, vol. 102, Published for the Conference Board of the Mathematical Sciences, Washington, DC, by the Amer. Math. Soc., Providence, RI, 2004. MR 2020489 (2005c:11053) - 11.
- S. Ramanujan, On certain arithmetical functions, Trans. Camb. Phil. Soc. 22 (1916), 159-184 (Collected Papers, No. 18).
- 12.
- O. Richter, The action of the heat operator on Jacobi forms, to appear in the Proceedings of the AMS.
- 13.
- J-P. Serre, Formes modulaires et fonctions zeta
 -adiques, in: Modular functions of one variable III, Lecture Notes in Math. 350, pp. 191-268, Springer, 1973. MR 0404145 (53:7949a) - 14.
- A. Sofer,
 -adic aspects of Jacobi forms, J. Number Theory 63 (1997), no. 2, 191-202. MR 1443756 (98b:11058) - 15.
- H. P. F. Swinnerton-Dyer, On
 -adic representations and congruences for coefficients of modular forms, in: Modular functions of one variable III, Lecture Notes in Math. 350, pp. 1-55, Springer, 1973. MR 0406931 (53:10717a)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
11F50,
11F60
Retrieve articles in all Journals with MSC
(2000):
11F50,
11F60
Additional Information:
Olav
K.
Richter
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203
Email:
richter@unt.edu
DOI:
10.1090/S0002-9939-08-09274-5
PII:
S 0002-9939(08)09274-5
Received by editor(s):
June 25, 2007
Posted:
April 15, 2008
Communicated by:
Ken Ono
Copyright of article:
Copyright
2008,
American Mathematical Society
|
Comments: webmaster@ams.org