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 mathematics, the Hecke algebra is the algebra generated by Hecke operators, which are named after Erich Hecke. The algebra is a commutative ring. In...

published in 2012:. The Hecke algebra may also be reduced modulo 2. It is defined to be the algebra generated by Hecke operators modulo 2, over F 2 {\displaystyle...

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. Hecke was...

(meaning simultaneous Hecke eigenform with modular group SL(2,Z)) is a modular form which is an eigenvector for all Hecke operators Tm, m = 1, 2, 3, .....

Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group. Hecke algebras...

ship A minced oath for "hell" Hecke may refer to: Hecke algebra (disambiguation) Hecke character Hecke operator Hecke (surname) This disambiguation page...

classical Hecke algebra, which is the commutative ring of Hecke operators in the theory of modular forms. The case leading to the Iwahori–Hecke algebra...

In mathematics, a Hecke algebra is classically the algebra of Hecke operators studied by Erich Hecke. It may also refer to one of several algebras generalizing...

L-function of a modular curve at a prime p in terms of the eigenvalues of Hecke operators. It was introduced by Eichler (1954) and generalized by Shimura (1958)...

≈ d mod N. The diamond operators form an abelian group and commute with the Hecke operators. In Unicode, the diamond operator is represented by the character...

Hecke, a German mathematician. Hecke algebra Hecke algebra of a locally compact group Hecke algebra of a finite group Hecke algebra of a pair Hecke polynomial...

ZD, the limit of the system Z/pnD. Consider any eigenfunction of the Hecke operator Tp with eigenvalue λp prime to p. We describe a procedure for deriving...

of Halle. A Brandt matrix is a computational way of describing the Hecke operator action on theta series as modular forms. The theory was developed in...

in the traces of Hecke operators was linked to the Eichler–Selberg trace formula, of Selberg and Martin Eichler, for a Hecke operator acting on a vector...

function Weil conjectures Modular form modular group Congruence subgroup Hecke operator Cusp form Eisenstein series Modular curve Ramanujan–Petersson conjecture...

arise at a given integer level N in such a way that the theory of Hecke operators can be extended to higher levels. Atkin–Lehner theory is based on the...

étale cohomology theory were being worked out. In 1937, Erich Hecke used Hecke operators to generalize the method of Mordell's proof of the first two conjectures...

of a modular curve, consisting roughly of elements of the Hecke algebra of Hecke operators that annihilate the Eisenstein series. It was introduced by...

between modular forms and number theory is furnished by the theory of Hecke operators, which also gives the link between the theory of modular forms and...

non-abelian. A classical example is the product of two Hecke operators. This is the product in the Hecke algebra, which is commutative even though the group...

the shift in emphasis is that the Hecke operators are here in effect put on the same level as the Casimir operators; which is natural from the point of...

Petersson inner product is a positive definite Hermitian form. For the Hecke operators T n {\displaystyle T_{n}} , and for forms f , g {\displaystyle f,g}...

examples, even when V and W are algebraic curves: for example the Hecke operators of modular form theory may be considered as correspondences of modular...

The proof was by means, in effect, of the Hecke operators, which had not yet been named after Erich Hecke; it was, in retrospect, one of the major advances...

distinguished operators called Hecke operators on smooth functions on congruence covers, which commute with each other and with the Laplace–Beltrami operator and...

Induced representation Peter–Weyl theorem Spherical harmonic Casimir operator Hecke operator Stone–von Neumann theorem Discrete series representation Tempered...

weight two and level N and is also an eigenform (an eigenvector of all Hecke operators); this is the Hasse–Weil conjecture, which follows from the modularity...

generators and relations. The identity is proved using the fact that Hecke operators applied to J yield polynomials in J. By comparing root multiplicities...

The resulting representation is not usually 2-dimensional, but the Hecke operators cut out a 2-dimensional piece. It is easy to demonstrate that these...