hecke operator造句

• Hecke operators can be realized in a number of contexts.
• A classical example is the product of two Hecke operators.
• Hecke operators may be studied geometrically, as correspondences connecting pairs of modular curves.
• Another way to express Hecke operators is by means of double cosets in the modular group.
• Algebras of Hecke operators are called "'Hecke algebras "', and are commutative rings.
• A Brandt matrix is a computational way of describing the Hecke operator action on theta series as modular forms.
• Other, related, mathematical rings are called Hecke algebras, although the link to Hecke operators is not entirely obvious.
• Therefore, the spectral theorem implies that there is a basis of modular forms that are eigenfunctions for these Hecke operators.
• The Hecke algebra of Hecke operators acting on the cusp form ? is just isomorphic to "'Z " '.
• Used Hecke operators on modular forms in a paper on the special cusp form of Ramanujan, ahead of the general theory given by.
• The idea goes back to earlier work of Adolf Hurwitz, who treated algebraic correspondences between modular curves which realise some individual Hecke operators.
• In 1917 L . Mordell proved the first two relations using techniques from complex analysis, specifically what are now known as Hecke operators.
• As the function " f " is also an eigenvector under each Hecke Operator " T i ", it has a corresponding eigenvalue.
• The crucial conceptual link 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 representation theory.
• Suppose that " T " * is the ring generated by the Hecke operators acting on all modular forms for ? 0 ( " N " ) ( not just the cusp forms ).
• His research deals with the multiplicative arithmetic of quadratic forms, zeta functions of automorphic forms, modular forms in several variables ( such as Siegel modular forms, Hecke operators, spherical functions, and theta functions.
• These come from the Hecke operator, considered first as an algebraic correspondence on " X ", and from there as acting on divisor classes, which gives the action on " J ".
• There is also a collection of distinguished operators called Hecke operators on smooth functions on congruence covers, which commute with each other and with the Laplace & ndash; Beltrami operator and are diagonalisable in each eigenspace of the latter.
• Similarly Spec ( " T " * ) contains a line ( called the Eisenstein line ) isomorphic to Spec ( "'Z "') coming from the action of Hecke operators on the Eisenstein series.
• The Hecke operators, which act on the space of all cusp forms, preserve the subspace of newforms and are spectral theory of such operators, there exists a basis for the space of newforms consisting of eigenforms for the full Hecke algebra.