In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by Erich Hecke (1937a,1937b), 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.

Erich Hecke (20 September 1887 – 13 February 1947) was a German mathematician known for his work in number theory and the theory of modular forms.

Erich Hecke was a Polish-born German mathematician whose best work was in analytic number theory. Erich Hecke's father, Heinrich Hecke, was an architect. Erich attended primary school at Buk before going to Posen for his secondary school studies. He graduated from secondary school in 1905 and in that year he entered the University of Breslau.

A Hecke character is a character of the idele class group of a number field or global function field. It corresponds uniquely to a character of the idele group which is trivial on principal ideles, via composition with the projection map.

In this paper, we aim to discuss Hecke operators in the theory of modular forms. We will show how the Hecke ring H(GL 2(Q p);GL 2(Z p)), the ring of all locally constant, compactly supported GL 2(Z p)-bi-invariant functions f : GL 2(Q p) ! C, is associated with the Hecke operator attached to p. To do so, we will rst

2024年2月15日 · There are Hecke operators in much more general settings, e.g. for suitable subgroups of the modular group $\Gamma$. A quite abstract group setting follows, [a6] . Let $G$ be a group and $D$ a subgroup.

5 天之前 · A family of operators mapping each space M_k of modular forms onto itself. For a fixed integer k and any positive integer n, the Hecke operator T_n is defined on the set M_k of entire modular forms of weight k by (T_nf)(tau)=n^(k-1)sum_(d|n)d^(-k)sum_(b=0)^(d-1)f((ntau+bd)/(d^2)).

2016年6月16日 · I think of Hecke operators when interpreted as double coset operators as solving a relatively easy question in representation theory. For simplicity let $G$ be a finite group and $M$ be a complex vector space on which $G$ acts from the right.

Hecke is a software package for algebraic number theory maintained by Claus Fieker and Tommy Hofmann. It is written in julia and is based on the computer algebra packages Nemo and AbstractAlgebra.

1 Hecke Operators 1.1 Classical Setting First, we will recall the classical theory of Hecke operators. Let be a congruence subgroup of GL+ 2 (R) and f2M k(N). Recall the operation of on M k(N) is given by: (fj k)(z) = f az+ b cz+ d p det cz+ d! k The space of Hecke Operators H is defined to be the free abelian group generated by the double ...