Kneser— Hecke— operators in coding theory

Kneser-Hecke-operators in coding theory

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...

Se p 20 05 An analogue of Hecke - operators in coding theory

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...

Hecke Operators

Hecke Operators on Cohomology

Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke operators are introduced includes the group cohomology of discrete subgroups of a semisimple Lie group, the de Rham c...

Hecke Operators on Rational Functions

Contents 1. Introduction 1 2. Some preliminaries 5 3. The point spectrum of U p 7 4. A structure theorem for eigenfunctions 14 5. A decomposition into finite dimensional eigenspaces 21 6. Simultaneous eigenfunctions 23 7. A first application: tensor products of Hecke operatorsand the Riemann zeta function 27 8. A second application: completely multiplicative coefficients 30 9. Appendix: Explici...