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Construction of entire modular forms of weights 5 and 6 for the congruence group Γ0(4N)

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Abstract

Two classes of entire modular forms of weight 5 and two of weight 6 are constructed for the congruence subgroup Γ0(4N). The constructed modular forms as well as the modular forms from [1] will be helpful in the theory of representation of numbers by the quadratic forms in 10 and 12 variables.

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References

  1. 1.

    G. Lomadze, On some entire modular forms of weights 5 and 6 for the congruence group Γ0(4N).Georgian Math. J. 1(1994), No. 1, 53–76.

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Lomadze, G. Construction of entire modular forms of weights 5 and 6 for the congruence group Γ0(4N). Georgian Mathematical Journal 2, 189–199 (1995). https://doi.org/10.1007/BF02257478

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1991 Mathematics Subject Classification

  • 11F11
  • 11F03
  • 11F27

Key words and phrases

  • Quadratic form
  • entre modular form
  • congruence subgroup
  • theta-series
  • generalized Gauss' sum