- In mathematics, an
eigenform (meaning
simultaneous Hecke eigenform with
modular group SL(2,Z)) is a
modular form
which is an
eigenvector for all Hecke...
- form f is a
simultaneous eigenform of all
Hecke operators Tm with
eigenvalues λm then am = λma1 and a1 ≠ 0.
Hecke eigenforms are
normalized so that a1...
-
suited to the
organization mankind discovers in nature." The
notion of
eigenform is an
example of a self-referential
system that
produces a
stable form...
- to all
automorphic zeta functions, such as
Mellin transforms of
Hecke eigenforms.
Artin (1924)
introduced global zeta
functions of (quadratic) function...
- to cusp
forms and Ma**** forms. For the case of cusp forms, each
Hecke eigenform (newform)
corresponds to a
cuspidal representation. Let G be a reductive...
-
Hecke eigenforms of
weight 2. The 1-dimensional
factors are
elliptic curves (there can also be higher-dimensional factors, so not all
Hecke eigenforms correspond...
-
obvious is that
given a
modular form of a
certain special type, a
Hecke eigenform with
eigenvalues in Q {\displaystyle \mathbf {Q} } , one also gets a homomorphism...
- "Eigen-" in
composita such as eigenfunction, eigenvector, eigenvalue,
eigenform; in
English "self-" or "own-". They are
related concepts in the fields...
- second-order
cybernetics and also
features in
economics with Kauffman's
Eigenform of markets.
MacKenzie noted that the
study of
economics does more than...
- of
complex conjugation has
determinant -1. To any
normalized modular eigenform f = q + a 2 q 2 + a 3 q 3 + ⋯ {\displaystyle f=q+a_{2}q^{2}+a_{3}q^{3}+\cdots...
