- combinatorics, and physics. A
common example of an
eigenform, and the only non-cuspidal
eigenforms, are the
Eisenstein series.
Another example is the...
- 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...
-
Foerster 2003, p. 301.
Foerster 2003, p. 289. Kauffman, L. H. (2003). "
Eigenforms:
Objects as
tokens for eigenbehaviors."
Cybernetics and
Human Knowing...
-
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...
- to all
automorphic zeta functions, such as
Mellin transforms of
Hecke eigenforms.
Artin (1924)
introduced global zeta
functions of (quadratic) function...
- Research. In the two
papers based on his Ph.D. thesis, "Curvature and
Eigenforms of the
Laplace Operator" (Journal of
Differential Geometry), and "An Analytical...
- {\displaystyle \mathrm {SL} _{2}(\mathbb {R} )} as
modular forms. They are
eigenforms of the
hyperbolic Laplace operator Δ {\displaystyle \Delta }
defined on...
-
obvious is that
given a
modular form of a
certain special type, a
Hecke eigenform with
eigenvalues in Q {\displaystyle \mathbb {Q} } , one also gets a homomorphism...
-
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...
- R.
Holowinsky and K. Soundararajan, "M****
equidistribution for
Hecke eigenforms," arXiv:0809.1636v1 K. Soundararajan, "Nonvanishing of
quadratic Dirichlet...
