Zhu Xiao-lin
Abstract
Based on the research of modular form theory,it is explicitly proved that modular form space and its cusp form subspace are invariant under Hecke operations.The explicit formula of the changes of Fourier coefficient between the modular form and the new form obtained by Hecke operation is also gotten.
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Based on the research of modular form theory,it is explicitly proved that modular form space and its cusp form subspace are invariant under Hecke operations.The explicit formula of the changes of Fourier coefficient between the modular form and the new form obtained by Hecke operation is also gotten.
Key concepts: Hecke operator, Modular form, Cusp form, Modular design, Mathematics, Invariant (physics), Pure mathematics, Cusp (singularity)