His early work included establishing the functional equation for the Dedekind zeta function, with a proof based on theta functions. The method extended to the L-functions associated to a class of characters now known as Hecke characters or idele class characters: such L-functions are now known as Hecke L-functions.
In mathematics, in particular in the theory of modular forms, a Hecke operator is a certain kind of 'averaging' operator that plays a significant role in the structure of vector spaces of modular forms (and more general automorphic representations).
The theory of Hecke operators on modular forms is often said to have been founded by Mordell in a paper on the special cusp form of Ramanujan, ahead of the general theory given by ErichHecke.
In the classical elliptic modular form theory it is shown that the Hecke operators are a C-star algebra with respect to the Peterson inner product; and that therefore the spectral theory implies that there is a basis of modular forms that are eigenfunctions for all Hecke operators.
ErichHecke (September 20, 1887 – February 13, 1947) was a German mathematician.
He devoted most of his research to the theory of modular forms, creating the general theory of cusp forms (holomorphic, for GL(2)), as it is now understood in the classical setting.
The method extended to the L-functions associated to a class of characters now known as Hecke characters or idele class characters: such L-functions are now known as HeckeL-functions.
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