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

Famous quotes containing the word history:

“At present cats have more purchasing power and influence than the poor of this planet. Accidents of geography and colonial history should no longer determine who gets the fish.”
—Derek Wall (b. 1965)

“In every election in American history both parties have their clichés. The party that has the clichés that ring true wins.”
—Newt Gingrich (b. 1943)

“We may pretend that we’re basically moral people who make mistakes, but the whole of history proves otherwise.”
—Terry Hands (b. 1941)