Duke Mathematical Journal

Nonvanishing modulo $\ell$ of Fourier coefficients of half-integral weight modular forms

Jan Hendrik Bruinier

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 98, Number 3 (1999), 595-611.

Dates
First available: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077228361

Mathematical Reviews number (MathSciNet)
MR1695803

Zentralblatt MATH identifier
0966.11019

Digital Object Identifier
doi:10.1215/S0012-7094-99-09819-8

Subjects
Primary: 11F30: Fourier coefficients of automorphic forms
Secondary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50] 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Citation

Bruinier, Jan Hendrik. Nonvanishing modulo ℓ of Fourier coefficients of half-integral weight modular forms. Duke Mathematical Journal 98 (1999), no. 3, 595--611. doi:10.1215/S0012-7094-99-09819-8. http://projecteuclid.org/euclid.dmj/1077228361.


Export citation

References

  • [B] J. H. Bruinier, On a theorem of Vignéras, Abh. Math. Sem. Univ. Hamburg 68 (1998), 163–168.
  • [Ca] L. Carlitz, Arithmetic properties of generalized Bernoulli numbers, J. Reine Angew. Math. 202 (1959), 174–182.
  • [Ci] Barry A. Cipra, On the Niwa-Shintani theta-kernel lifting of modular forms, Nagoya Math. J. 91 (1983), 49–117.
  • [Co] Henri Cohen, Sums involving the values at negative integers of $L$-functions of quadratic characters, Math. Ann. 217 (1975), no. 3, 271–285.
  • [DR] P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1973, 143–316. Lecture Notes in Math., Vol. 349.
  • [H1] Kuniaki Horie, A note on basic Iwasawa $\lambda$-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), no. 1, 31–38.
  • [H2] Kuniaki Horie, Trace formulae and imaginary quadratic fields, Math. Ann. 288 (1990), no. 4, 605–612.
  • [HO] Kuniaki Horie and Yoshihiro Ônishi, The existence of certain infinite families of imaginary quadratic fields, J. Reine Angew. Math. 390 (1988), 97–113.
  • [J] N. Jochnowitz, Congruences between modular forms of half integral weights and implications for class numbers and elliptic curves, preprint.
  • [Ka] Nicholas M. Katz, $p$-adic properties of modular schemes and modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1973, 69–190. Lecture Notes in Mathematics, Vol. 350.
  • [Ko1] Winfried Kohnen, Fourier coefficients of modular forms of half-integral weight, Math. Ann. 271 (1985), no. 2, 237–268.
  • [Ko2] W. Kohnen, A simple remark on eigenvalues of Hecke operators on Siegel modular forms, Abh. Math. Sem. Univ. Hamburg 57 (1987), 33–35.
  • [KoZ] W. Kohnen and D. Zagier, Values of $L$-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), no. 2, 175–198.
  • [MW] B. Mazur and A. Wiles, Class fields of abelian extensions of $\bf Q$, Invent. Math. 76 (1984), no. 2, 179–330.
  • [N] Shinji Niwa, Modular forms of half integral weight and the integral of certain theta-functions, Nagoya Math. J. 56 (1975), 147–161.
  • [OS] Ken Ono and Christopher Skinner, Fourier coefficients of half-integral weight modular forms modulo $l$, Ann. of Math. (2) 147 (1998), no. 2, 453–470.
  • [SS] J.-P. Serre and H. M. Stark, Modular forms of weight $1/2$, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976), Springer, Berlin, 1977, 27–67. Lecture Notes in Math., Vol. 627.
  • [Sh1] Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, 1971.
  • [Sh2] Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481.
  • [St] Jacob Sturm, Theta series of weight $3/2$, J. Number Theory 14 (1982), no. 3, 353–361.
  • [V] M.-F. Vignéras, Facteurs gamma et équations fonctionnelles, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976), Springer, Berlin, 1977, 79–103. Lecture Notes in Math., Vol. 627.
  • [W] J.-L. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. (9) 60 (1981), no. 4, 375–484.