Modular forms of half-integral weight with few non-vanishing coefficients modulo

Author:
D. Choi

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2683-2688

MSC (2000):
Primary 11F11, 11F33

DOI:
https://doi.org/10.1090/S0002-9939-08-09195-8

Published electronically:
March 27, 2008

MathSciNet review:
2399029

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Abstract: Bruinier and Ono classified cusp forms of half-integral weight

**1.**S. Ahlgren and M. Boylan,*Arithmetic properties of the partition function*. Invent. Math. 153(3):487-502, 2003. MR**2000466 (2004e:11115)****2.**S. Ahlgren and M. Boylan,*Coefficients of half-integral weight modular forms modulo*. Math. Ann. 331(1):219-239, 2005. MR**2107445 (2005k:11091)****3.**Antal Balog, Henri Darmon and Ken Ono,*Congruence for Fourier coefficients of half-integral weight modular forms and special values of -functions*. (English summary) Analytic number theory, Vol. 1 (Allerton Park, IL, 1995), 105-128, Progr. Math., 138, Birkhäuser Boston, Boston, MA, 1996. MR**1399333 (97e:11056)****4.**Jan Hendrik Bruinier,*Non-vanishing modulo of Fourier coefficients of half-integral weight modular forms*. Duke Math. J. 98(3):595-611, 1999. MR**1695803 (2000d:11061)****5.**J. H. Bruinier and K. Ono,*Coefficients of half-integral weight modular forms,*J. Number Theory 99(1): 164-179, 2003. MR**1957250 (2004b:11056)****6.**Benedict H. Gross,*A tameness criterion for Galois representations associated to modular forms*. Duke Math. J. 61(2):445-517, 1990. MR**1074305 (91i:11060)****7.**K. Ono,*The web of modularity: Arithmetic of the coefficients of modular forms and -series*, CBMS Regional Conf. Series in Math., vol. 102, Amer. Math. Soc., 2004. MR**2020489 (2005c:11053)****8.**Ken Ono, Christopher Skinner,*Fourier coefficients of half-integral weight modular forms modulo*, Ann. of Math. (2), 147(2):453-470, 1998. MR**1626761 (99f:11059a)****9.**Ken Ono, Christopher Skinner,*Corrigendum: ``Fourier coefficients of half-integral weight modular forms modulo ''*, Ann. of Math. (2), 148(1):361, 1998. MR**1652912 (99f:11059b)****10.**Jean-Pierre Serre,*Formes modulaires et fonctions zeta -adiques*(French). Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, 1972), pp. 191-268. Lecture Notes in Math., vol. 350, Springer, Berlin, 1973. MR**0404145 (53:7949a)****11.**H. P. F. Swinnerton-Dyer,*On -adic representations and congruences for coefficients of modular forms. Modular functions of one variable*, III (Proc. Internat. Summer School, Univ. Antwerp, 1972), pp. 1-55. Lecture Notes in Math., vol. 350, Springer, Berlin, 1973. MR**0406931 (53:10717a)**

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Additional Information

**D. Choi**

Affiliation:
School of Mathematics, KIAS, 207-43 Cheongnyangni 2-dong 130-722, Korea

Email:
choija@postech.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-08-09195-8

Keywords:
Modular forms,
congruences

Received by editor(s):
January 12, 2007

Received by editor(s) in revised form:
April 24, 2007

Published electronically:
March 27, 2008

Communicated by:
Ken Ono

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.