Upper Bounds for the Level of Normal Subgroups of Hecke Groups

DEMİRCİ M., Yurttas A., CANGÜL İ. N.

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Halkidiki, Yunanistan, 19 - 25 Eylül 2011, cilt.1389 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 1389
  • Doi Numarası: 10.1063/1.3636733
  • Basıldığı Şehir: Halkidiki
  • Basıldığı Ülke: Yunanistan
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In [4], Greenberg showed that n <= 6t(3) so that mu - nt <= 6t(4) for a normal subgroup N of level n and index mu having t parabolic classes in the modular group Gamma. Accola, [1], improved these to n <= 6t(2) always and n <= t(2) if Gamma/N is not abelian. In this work we generalise these results to Hecke groups. We get results between three parameters of a normal subgroup, i.e. the index mu, the level n and the parabolic class number t. We deal with the case q = 4, and then obtain the generalisation to other q. Two main problems here are the calculation of the number of normal subgroups and the determination of the bounds on the level n for a given t.