Hecke operators on Γ0(m)

@article{Atkin1970HeckeOO,
  title={Hecke operators on $\Gamma$0(m)},
  author={A. O. L. Atkin and Joseph Lehner},
  journal={Mathematische Annalen},
  year={1970},
  volume={185},
  pages={134-160}
}

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References

SHOWING 1-10 OF 16 REFERENCES

The Theory of Matrices

  • L. Mirsky
  • Mathematics
    The Mathematical Gazette
  • 1961
In the last two decades Soviet m athem aticians have produced a series of rem arkable books, whose common feature is the stress laid on thoroughness and intelligibility ra the r than on slickness of

Lectures on modular forms

Report consisting of an expository account of the theory of modular forms and its application to number theory and analysis.

The Normalizer Of Certain Modular Subgroups

  • M. Newman
  • Mathematics
    Canadian Journal of Mathematics
  • 1956
Introduction. Let G denote the multiplicative group of matrices where a, b, c, d are integers and ad — bc = 1. G is one of the well-known modular groups. Let G0(n) denote the subgroup of G