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...

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

(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, .....

≈ 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...

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...

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

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...

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 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...

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...

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...

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)...

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...

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...

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...

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...

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...

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...

by Goro Shimura (1973). It has the property that the eigenvalue of a Hecke operator Tn2 on F is equal to the eigenvalue of Tn on f. Let f {\displaystyle...

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...

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

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...

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

representation Peter–Weyl theorem Young tableau Spherical harmonic Hecke operator Representation theory of the symmetric group Representation theory of...

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

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...

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...

different from those taken directly from elliptic function theory. Hecke operators may be studied geometrically, as correspondences connecting pairs of...