Hecke Operator - History

History

Mordell (1917) used Hecke operators on modular forms in a paper on the special cusp form of Ramanujan, ahead of the general theory given by Hecke (1937). Mordell proved that the Ramanujan tau function, expressing the coefficients of the Ramanujan form,

$\Delta(q)=q\left(\prod_{n=1}^{\infty}(1-q^n)\right)^{24}= \sum_{n=1}^{\infty} \tau(n)q^n, \quad q=e^{2\pi i\tau},$

is a multiplicative function:

The idea goes back to earlier work of Hurwitz, who treated algebraic correspondences between modular curves which realise some individual Hecke operators.

Read more about this topic: Hecke Operator

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