Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

CONGRUENCE PROPERTIES OF COEFFICIENTS OF MODULAR FORMS FOR Γ+0(5)

  • Choi, SoYoung (Department of Mathematics Education Dongguk University-Gyeongju)
  • Received : 2013.10.14
  • Accepted : 2013.11.05
  • Published : 2013.11.15
Download PDF
⟨ Previous Next ⟩

Abstract

We find congruence properties on the coefficients of modular forms for ${\Gamma}^+_0(5)$ generated by ${\Gamma}_0(5)$ and a Fricke involution $\(_{5\;0}^{0\;-1}\)$.

Keywords

References

  1. Y. J. Choie, W. Kohnen, and K. Ono, Linear relations between modular form coeffcients and non-ordinary primes, Bull. London Math. Soc. 37 (2005), no. 3, 335-341. https://doi.org/10.1112/S0024609305004285
  2. T. Miyake, Modular forms, Translated from the 1976 Japanese original by Yoshitaka Maeda. Reprint of the first 1989 English edition. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2006. x+335 pp. ISBN: 978-3-540-29592-1; 3-540-29592-5.
  3. K. Ono, The web of modularity: arithmetic of the coeffcients of modular forms and q-series, CBMS Regional Conference Series in Mathematics, 102. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2004. viii+216 pp. ISBN: 0-8218-3368-5.
  4. J. Shigezumi, On the zeros of the Eisenstein series for ${\Gamma}^{\ast}_0$ (5) and ${\Gamma}^{\ast}_0$ (7). Kyushu J. Math. 61 (2007), no. 2, 527-549. https://doi.org/10.2206/kyushujm.61.527
  5. W. Stein, Modular forms, a computational approach, With an appendix by Paul E. Gunnells. Graduate Studies in Mathematics, 79. American Mathematical Society, Providence, RI, 2007. xvi+268 pp. ISBN: 978-0-8218-3960-7; 0-8218-3960-8.

Cited by

  1. ARITHMETIC OF MODULAR FORMS vol.30, pp.4, 2017, https://doi.org/10.14403/jcms.2017.30.4.445